Joe Biden saluted a “monumental step forward as a nation” on Saturday, after House Democrats finally reached agreement and sent a $1tn infrastructure package to his desk to be signed, a huge boost for an administration which has struggled for victories.

“This is a blue-collar blueprint to rebuild America,” Biden said, “and it’s long overdue.”

There was also a setback, however, as Democrats postponed a vote on an even larger bill. That 10-year, $1.85tn spending plan to bolster health, family and climate change programmes, known as Build Back Better, was sidetracked after centrists demanded a cost estimate from the Congressional Budget Office (CBO). Biden said he was confident he could get it passed.

Walking out to address reporters at the White House, the president began with a joke at the expense of his predecessor, Donald Trump.

“Finally, it’s infrastructure week,” he said.

Under Trump, the administration’s failure to focus on infrastructure amid constant scandal became a national punchline.

“We’re just getting started,” Biden said. “It is something that’s long overdue but long has been talked about in Washington but never actually been done.

“The House of Representatives passed an Infrastructure Investment and Jobs Act. That’s a fancy way of saying a bipartisan infrastructure bill, once-in-a-generation investment that’s going to create millions of jobs, modernise our infrastructure, our roads, our bridges, our broadband, a range of things turning the climate crisis into an opportunity, and a put us on a path to win the economic competition of the 21st century that we face with China and other large countries in the rest of the world.”

The House approved the $1tn bill late on Friday, after Democrats resolved a months-long standoff between progressives and centrists. The measure passed 228-206. Thirteen Republicans, mostly moderates, supported the bill while six progressive Democrats opposed it, among them Alexandria Ocasio-Cortez of New York.

Approval sent the bill to the desk of a president whose approval ratings have dropped and whose party struggled in elections this week. Biden said he would not sign the bill this weekend because he wanted those who passed it to be there when he did so.

“We’re looking more forward to having shovels in the ground,” Biden said. “To begin rebuilding America.

“For all of you at home, who feel left behind and forgotten in an economy that’s changing so rapidly, this bill is for you. The vast majority of those thousands of jobs that will be created don’t require a college degree. There’ll be jobs in every part of the country: red states, blue states, cities, small towns, rural communities, tribal communities.

“This is a blue-collar blueprint to rebuild America, and it’s long overdue.”

This week, Democratic candidates for governor lost in Virginia and squeaked home in New Jersey, two blue-leaning states. Those setbacks made leaders, centrists and progressives impatient to demonstrate they know how to govern a year before midterm elections that could see Republicans retake Congress.

At the White House, Biden said: “Each state is different and I don’t know but I think the one message that came across was, ‘Get something done … stop talking, get something done.’ And so I think that’s what the American people are looking for.

“All the talk about the elections and what do they mean? They want us to deliver. Democrats, they want us to deliver. Last night we proved we can on one big item. We delivered.”

The postponement of a vote on the spending bill dashed hopes of a double win. But in a deal brokered by Biden and party leaders, five moderates agreed to back the bill if CBO estimates of its costs are consistent with numbers from the White House and congressional analysts.

The agreement, in which lawmakers promised to vote by the week of 15 November, was a significant step towards shipping the bill to the Senate. Its chances there are not certain: it must pass on the casting vote of Vice-President Kamala Harris and with the approval of Joe Manchin of West Virginia and Kyrsten Sinema of Arizona, centrists who have proved obstructive so far.

The spending bill “is fiscally responsible”, Biden said. “That’s a fancy way of saying it is fully paid for. It doesn’t raise the deficit by a single penny. And it actually reduces the deficit according to the leading economists in this country over the long term. And it’s paid for by making sure that the wealthiest Americans, the biggest corporations begin to pay their fair share.”

Republicans have highlighted what they say will be the bill’s effects on dangerous economic inflation.

“According to economists,” Biden said, “this is going to be easing inflationary pressures … by lowering costs for working families.”

He also said: “We got out of the blue a couple of weeks ago a letter from 17 Nobel prize winners in economics and they determined that [the two bills] will ease inflationary pressures not create them.”

Biden acknowledged that he will not get Republican votes for the spending bill and must “figure out” how to unite his party. Friday was an exhausting day for Nancy Pelosi, the House speaker. She told reporters: “Welcome to my world. This is the Democratic party. We are not a lockstep party.”

Biden said he was confident he could find the votes. Asked what gave him that confidence, the president alluded to his legislative experience as a senator and vice-president, saying: “Me.”

On Friday night, Biden and his wife, Jill Biden, delayed travel to Delaware as the president worked the phones. Pramila Jayapal of Washington state, leader of the Congressional Progressive Caucus, told reporters Biden even called her mother in India. It was unclear why.

“This was not to bribe me, this is when it was all done,” Jayapal said, adding that her mother told her she “just kept screaming like a little girl”.

• Associated Press contributed to this report