Joseph R. Biden Jr. had just been sworn in as vice president. All he needed now was a job.

During the 2008 campaign, Barack Obama had assured Mr. Biden that he would be consulted on every major decision. But many on the new president’s team were still Biden-skeptical, and Mr. Obama was not sure the meandering former senator had the discipline to be an effective governing partner, people close to both men said.

So, during a private lunch in February 2009, Mr. Biden slid a memo across the table to Mr. Obama, outlining a role to erase those doubts: quarterbacking the implementation of the $787 billion economic stimulus that had been rammed through Congress a few days earlier in the depths of recession.

“Sounds good to me,” said Mr. Obama, barely glancing at the memo, according to two people familiar with the exchange.

Mr. Obama was already pivoting to health care reform, so why not encharge Mr. Biden? As it turned out, Mr. Biden’s work on the rollout, implementation, oversight and selling of the 2009 stimulus — officially the American Recovery and Reinvestment Act — was the most sustained, and perhaps the most significant, assignment of his time in office.

Eleven years later, in an election season defined by pandemic, economic collapse and a far-larger relief package, Mr. Biden’s campaign is hoping to leverage his stewardship of the 2009 stimulus as a point of contrast with President Trump — whose White House is pushing back at congressional oversight of $2.7 trillion in new spending even as a host of problems has emerged, especially chaos in the small-business loan program.

“The central question of this election will be who can dig us out of a historic economic hole, so his leadership of the recovery act should be his core résumé selling point,” said David Plouffe, Mr. Obama’s top political adviser and a Biden surrogate.

An examination of that critical two-year period, drawn from interviews with 30 people involved in the effort, offers a glimpse of Mr. Biden’s strengths as a manager — his enthusiasm, focus on detail and knack for leading a first-rate team that moved the money out quickly and minimized waste and fraud. It was “one big competence test,” and Mr. Biden aced it, his longtime lieutenant, Ron Klain, said in an interview.

But the stimulus says more about the kind of vice president Mr. Biden was than about the kind of president he would be. While he became the expediter-in-chief and offered Mr. Obama advice and tactical suggestions, he made none of the major strategic calls about the size and composition of the program, aides said. Nor did he seriously push Mr. Obama — as he is now pressuring Mr. Trump — to fight for a bigger funding package, even though former officials said he conceded the stimulus was probably too small.

There was nothing ambiguous, though, about the impact of the stimulus on Mr. Biden’s political fortunes.

“It sort of made him, to be honest, in the eyes of the Obama people,” said Ray LaHood, a former Republican congressman who served as Mr. Obama’s transportation secretary.

Mr. Obama picked Mr. Biden, in part, because he viewed him as a past-tense presidential aspirant. Yet if overseeing the stimulus proved Mr. Biden was a team player, his pursuit of the assignment — and he wanted it badly — was also a sign that he had never entirely abandoned his own political ambitions. In the end, the stimulus catalyzed his emergence as Mr. Obama’s trusted partner and, eventually, set him up as a presidential contender.

Mr. Biden mentioned the stimulus only in passing on the 2020 trail, when there was a trail, and has only recently begun invoking it as a campaign theme. There is broad agreement that the program had a positive impact on an economy in free fall, with the nonpartisan Congressional Budget Office concluding that it created between two million and 4.8 million full-time jobs.

But it left a bittersweet aftertaste, attacked by progressives as insufficiently bold and savaged by Republicans to this day as a boondoggle — with the Republican National Committee chairwoman, Ronna McDaniel, saying in an email last week that the stimulus “proves” Mr. Biden cannot run a government. For much of the public, however, it is a half-forgotten episode, wedged between the deeply unpopular Bush administration bank bailout and the polarizing war over Obamacare.

“The big problem, when you get right down it, is that we succeeded in making the situation less bad rather than good — so how do you sell that?” said Jared Bernstein, Mr. Biden’s top economic adviser during his vice presidency.

$787 Billion to Spend

The stimulus was born on a snow-sodden December day at Mr. Obama’s Chicago headquarters, a few weeks after the 2008 election.

There had been earlier talk of a smaller package, but the Obama economic team, led by Mr. Bernstein and Christina Romer, incoming chairwoman of the Council of Economic Advisers, said many, many hundreds of billions were needed immediately to prevent a second Great Depression.

Mr. Biden, participants recalled, spoke up for pro-worker provisions, funding for green energy projects and light rail. Later, he would intervene to insert $10 billion in additional funding for the National Institutes of Health. But he mainly supported the work of Mr. Bernstein, who played a central role in formulating the menu of infrastructure projects, payroll-tax cuts and aid to localities.

Mr. Obama’s top advisers were initially optimistic about winning Republican backing, telling aides to Nancy Pelosi, the speaker of the House, that they could secure up to 80 votes in the Senate. Mr. Biden knew better, telling the speaker and Mr. Obama they would snag four or five Republicans at most.

“Don’t listen to any of this happy-talk crap,” he said, according to a senior Obama adviser.

Ultimately three Republicans voted for the bill, and only after Mr. Biden helped wheedle a yes from his close friend Arlen Specter, a moderate from Pennsylvania.

Once the fight was over, Mr. Biden’s chief of staff, Mr. Klain, who had held the same post for Vice President Al Gore, drafted the implementation plan that Mr. Obama did not need to read. It amounted to a congenial power grab, giving Mr. Biden expansive influence over which projects, submitted by local officials and cabinet departments, would be funded.

Mr. Biden’s first priority, according to Mr. Klain, was creating a central management structure, aimed at avoiding the kind of confusion that has thus far plagued the financial response to the coronavirus crisis under Mr. Trump.

Mr. Klain and his team broke their mission into three parts: identifying “shovel-ready” projects, minimizing misuse of the funding (including the creation of an online transaction tracker, Recovery.gov) and trying to muster public enthusiasm.

Mr. Biden started by auditioning veteran state and federal officials for the 10-person operation that would oversee the effort, attacking the task with an abrasive impatience that belied his jovial “Uncle Joe” image. “He was a yeller,” one adviser recalled. He wanted an exemption from Obama administration rules that banned ex-lobbyists from being hired for their expertise, but was quickly shot down — although he often grumbled about it, another aide recalled.

A federal official who had business with the new vice president in early 2009 described the following the scene: Mr. Biden arrived 15 minutes late, ripped off his suit jacket and began rattling off questions in front of a roaring fire that turned his office into a furnace — to the stifling discomfort of his visitor, who did not have the option of taking off his coat.

He left much of the initial vetting of projects to his team, and spent much of his time pressuring mayors, governors and cabinet officials to accelerate work that would create jobs and momentum for the besieged administration.

“He was very impatient at first,” said G. Edward DeSeve, a veteran federal oversight specialist recruited by Mr. Biden. “But it didn’t take him too long to gain an understanding of just how big a task it was to run something on this scale.”

A frequent source of heartburn, aides said, was the water and sewer projects overseen by the Environmental Protection Agency, which were subject to an array of federal and local regulations. A multibillion-dollar effort to weatherize homes, considered a fast way to inject cash into the economy, became tangled in red tape, in part because of labor protections Mr. Biden had championed during the transition.

A marquee project in Mr. Biden’s birthplace state, Pennsylvania, was a $1.7 million replacement of the bridge over Conodoguinet Creek near Harrisburg. It, too, seemed like a straightforward-enough proposition, and Mr. Biden hoped to kick off a national barnstorming tour there within weeks.

No go, state officials shot back. The earliest date was several months out.

Nothing proved quite so nettlesome as the project closest to Mr. Biden’s heart. He had successfully lobbied to include $8 billion for high-speed rail projects, but his plans were slowed when two conservative Republican governors riding the Tea Party backlash, Rick Scott of Florida and Scott Walker of Wisconsin, rejected the cash.

“It would have required a major investment by the state at a time when we were dealing with our own budget crisis,” said Mr. Scott, now a senator, explaining his decision to turn down $2 billion for a route connecting Tampa and Orlando. The money was eventually diverted to other states.

The desire for speed contributed to what would become the centerpiece of Republican efforts to discredit the stimulus — the collapse of Solyndra, a California-based solar-panel manufacturer that went bankrupt after receiving $527 million in loan guarantees.

Mr. Biden’s advisers placed the blame on China, for glutting the market with cheap panels. But the nonpartisan Government Accountability Office, describing the rushed review process as “alarming,” concluded that the Energy Department had given preliminary loan approvals before completing detailed assessments of the company’s projects.

For all that, the episode was more exception than norm. By September 2010, a panel monitoring allegations of fraud and abuse concluded stimulus had a 0.2 percent incidence of waste and fraud. That finding was not seriously contested by Republican investigators in Congress, and an 18-month congressional inquiry into Solyndra found no evidence of malfeasance or favoritism.

Mixed Political Impact

Still, the drip-drip of Republican attacks was quickly turning the program into a political liability.

The sharpest attacks came from friends of the president and vice president, Senators Tom Coburn of Oklahoma and John McCain of Arizona, who began scouring Recovery.com for projects they deemed silly or wasteful, including an online dance course and a study of the effects of cocaine on monkeys.

Nitpicks weren’t the biggest problem, though. Numbers were.

Mr. Biden’s team achieved its goal of spending 70 percent, or roughly $550 billion, of the stimulus funding in the first 18 months. But it took longer than the White House had expected for its effects to be felt. Republicans seized on a January 2009 report in which Biden economic advisers had predicted unemployment would peak at around 8 percent under the stimulus. By October 2009 the rate had hit 10 percent, and it would not fall below the 8 percent benchmark until September 2012.

Mr. Obama’s own approval numbers were sagging, too. “The only thing that is more unpopular than me right now is the stimulus,” Mr. Obama tartly declared at a cabinet meeting around that time, as Mr. Biden listened in silence, according to a person in the room. Eventually, the president dropped the word “stimulus” from his speeches, one former adviser said.

Against that backdrop, Mr. Biden, anointed salesman of the stimulus, was crisscrossing the country trying to gin up excitement, and focusing on what he could control, like making sure the recovery act signs on highway projects were large enough to be seen by motorists. (He also viewed his trips to Midwestern battleground states as opportunities to cement his connection to blue-collar voters, should he ever run for president again, several people close to him said, and he would invoke the stimulus during the 2012 re-election campaign.)

At the same time, he was quietly pressuring Mr. Obama to take more public credit for the one element of the stimulus that put $400 to $800 in tax credits directly into people’s pockets. Writing a single check to taxpayers might have been better politics, but Mr. Obama’s economics working group decided it was better to distribute the money in small increments to encourage spending.

Mr. Klain was livid that the “nerds” had won the argument, a former aide said, and Mr. Biden turned to a plan from another old friend, Gov. Ed Rendell of Pennsylvania.

“Let’s have Treasury send a letter to every taxpayer saying, ‘President Obama wants you to spend this money immediately,’” Mr. Rendell recalled in a recent interview. “It wasn’t like Trump putting his name on the check, but it let people know Obama had done this thing for them.”

Mr. Biden brought the idea to Mr. Obama, and there it remained. “Jesus, that was dumb,” Mr. Rendell said.

By the fall of 2009, the external narrative — that the stimulus had significant economic value but little political currency — seemed set. At the same time, an internal narrative was falling into place: Joe Biden could be trusted.

It has proved to be a durable story line, at least inside the party. “Joe led with integrity, which is an enormous contrast from the current administration,” Senator Elizabeth Warren of Massachusetts, who cited the stimulus in her recent endorsement of Mr. Biden, wrote in an email.

Mr. Trump, whose 2017 national infrastructure plan collapsed because of inattention and muddled planning, has dismissed Mr. Biden’s work on the stimulus. “I haven’t heard of anything that’s been built,” he said last month.

The two coronavirus rescue packages differ from the Obama stimulus in significant ways, with most cash being sent directly to taxpayers and businesses. Still, both were backstops against economic calamity, and the new law contains accountability provisions modeled on the 2009 legislation.

But Mr. Trump has not embraced oversight as Mr. Obama did, nor has he deployed Vice President Mike Pence in the Biden watchdog role, leaving the task to various administration officials, like Treasury Secretary Steven Mnuchin.

This is not lost on Mr. Biden. Just as Mr. Trump signed the first coronavirus bill, an aide called to inform Mr. Biden that the president planned to resist crucial congressional oversight provisions on constitutional grounds.

Mr. Biden, already annoyed at having to campaign from his basement in Delaware, exploded: “What a joke! You’ve got to be kidding me!” he shouted, inserting expletives, according to two people who talked with him.