WASHINGTON — State and national voting-rights advocates are waging the most consequential political struggle over access to the ballot since the civil rights era, a fight increasingly focused on a far-reaching federal overhaul of election rules in a last-ditch bid to offset a wave of voting restrictions sweeping Republican-controlled state legislatures.

The federal voting bill, which passed in the House this month with only Democratic support, includes a landmark national expansion of voting rights, an end to partisan gerrymandering of congressional districts and new transparency requirements on the flood of dark money financing elections that would override the rash of new state laws.

The energy in support for it radiates from well-financed veteran organizers to unpaid volunteers, many who were called to political activism after former President Donald J. Trump’s upset win in 2016. It is engaging Democrats in Washington and voting rights activists in crucial states from Georgia to Iowa to West Virginia to Arizona — some facing rollbacks in access to the ballot, some with senators who will play pivotal roles and some with both.

But after approval of the Democratic bill in the House, the campaign to pass the For the People Act, designated Senate Bill 1, increasingly appears to be on a collision course with the filibuster. The rule requires 60 votes for passage of most legislation in a bitterly divided Senate, meaning that Republicans can kill the voting bill and scores of other liberal priorities despite unified Democratic control of Washington.

To succeed, Democrats will have to convince a handful of moderate holdouts to change the rules, at least for this legislation, with the likelihood that a single defection in their own party would doom their efforts. It is a daunting path with no margin for error, but activists believe the costs for failure, given the Republican limits on voting, would be so high that some accommodation on the filibuster could become inevitable.

Two left-leaning elections groups, the advocacy arm of End Citizens United and Let America Vote along with the National Democratic Redistricting Committee, plan this week to announce an infusion of $30 million to try to hasten the groundswell. The money will fund paid advertising in at least a dozen states and finance organizers to target Democratic and Republican swing senators in six of them.

“We are at a once-in-a-generation moment,” said Tiffany Muller, president of End Citizens United and Let America Vote. “We either are going to see one of the most massive rollbacks of our democracy in generations, or we have an opportunity to say: ‘No, that is not what America stands for. We are going to strengthen democracy and make sure everyone has an equal voice.’”

The sense of a pivotal moment is the one thing Democrats and Republicans agree on. Republicans are still inflamed by Mr. Trump’s false claims of a stolen election and the party’s unified message that voting restrictions, many of which fall most heavily on minorities and Democratic-leaning voters, are needed to prevent fraud, which studies have repeatedly shown to barely exist.

“This bill is the opposite of good governance — it’s a cynical attempt by the left to put their thumb on the scales of democracy and engineer our laws to help them win elections,” said Dan Conston, president of the Republican-aligned American Action Network. “They want to limit free speech, funnel public funds into their campaign accounts, seize from states the ability to run their own free and fair elections, and then spin it like this is really all about protecting voting rights.”

Ms. Muller and others are ostensibly focused on winning support for election legislation from 10 moderate Republican senators, including Lisa Murkowski of Alaska and Susan M. Collins of Maine.

But with Republican leaders promising near-unanimous opposition in the Senate, Democrats and their allies are positioning voting rights as the most persuasive case for scrapping or changing the filibuster that would limit much of Democrats’ legislative agenda.

“It is too important an issue and we are facing too big a crisis to let an arcane procedural motion hold back the passage of this bill,” Ms. Muller said. She argued that the rollback of voting rights was an existential threat to the democracy on which all other liberal causes, from gun control to health care reform, depend.

The urgency for federal action has mounted not just among Washington lobbyists and Democratic lawmakers, but grass roots groups that normally fight battles in state legislatures and city councils. Many spent the winter opposing the Republican voting agenda that included curbs on mail-in and early voting and stiffer voter ID requirements.

Lawmakers in Republican-controlled states have largely rebuffed those groups, leaving Democrats to see federal action as the only possible brake on widespread voting restrictions. At the same time, a handful of crucial Republican-led states are preparing to draw new state and congressional district maps in the fall that could further tilt power in their direction and lock Democrats out of a House majority for years.

Voting-rights proponents say they have not given up on stopping restrictive laws in states. The Arizona group Civic Engagement Beyond Voting, has already registered 2,000 people this year to testify remotely on proposed state legislation, with voting rights as a priority.

“People are up in arms,” said Cathy Kouts Sigmon, the group’s founder. “They’re relating these bills to how they vote and how members of their family vote.”

Voting-rights advocates in Georgia, who claim to have slowed or killed some restrictive bills, are aiming at local companies that have supported the bills’ sponsors, including Home Depot, Coca-Cola, Delta Air Lines and UPS. An advertising campaign led by voting and civil rights groups demands that the firms use their lobbying muscle in the Georgia statehouse to stop repressive voting bills instead of contributing to their Republican authors.

“They spent most of Black History Month peppering us with Martin Luther King quotes, but now that Blacks’ future is in jeopardy, they’re silent,” Nsé Ufot, the chief executive of one participant, the New Georgia Project, said last week. “We’re using digital ads, billboards, direct action at warehouses and call centers — we’re serious. This is urgent.”

One possible sign of some success: On Sunday, the Georgia Chamber of Commerce, whose members include those companies, expressed “concern and opposition” to restrictive clauses in two Republican bills.

Increasingly, though, the focus is on federal legislation. Ms. Sigmon’s group is recruiting Arizonans to lobby their senators on the elections bill. So are local chapters of Indivisible, a movement founded in response to Mr. Trump’s election, in Georgia and Arizona.

And so have national advocacy groups. Common Cause runs weeknight phone banks recruiting backers for the bill, and says it has generated 700,000 text messages supporting it. “It’s been a pretty incredible outpouring of support, because we all know what this moment means,” said Izzy Bronstein, the group’s national campaigns manager.

In Phoenix, the advocacy group Progress Arizona coordinates a statewide campaign to persuade Senator Kyrsten Sinema, a first-term Democrat, to drop her support of the filibuster. Among its tactics: billboards projected at night onto buildings and other spots, calling for an end to the filibuster and displaying the senator’s Capitol Hill phone number.

In Charleston, W. Va., Takeiya Smith of the advocacy group For West Virginia’s Future works with some 70 students at six state colleges to generate calls on Senate Bill 1 to Senators Shelley Capito, a Republican, and particularly Joe Manchin III, a Democrat whose support for the filibuster is a liberal target. The group plans daily campus events this week highlighting different parts of the measure. It is in turn allied with a national coalition, the Declaration for American Democracy, that has enrolled 190 organizations to push for its passage.

In Atlanta, the Black Voters Matter Fund is preparing with other groups a national campaign for Senate Bill 1 aimed at both senators and President Biden, who has expressed hope for the bill’s passage but has not actively worked for it.

“He’s got to have his Lyndon B. Johnson moment,” said Cliff Albright, the group’s executive director, referring to the former president’s arm-twisting on Capitol Hill for the Voting Rights Act in 1965.

“You’re president of the United States. You need to do more than hope that it passes,” he said of Mr. Biden. “He needs to use everything he’s learned over 47 years in Washington, D.C., to get this bill passed.”

Democrats first introduced the elections bill in 2019 as a catchall measure to address growing public disillusionment with dark money and corporate interests in politics. But as Republican state officials have raced to target voter participation, the bill’s voting provisions have increasingly been viewed by many on the left as essential protections to American democracy — and to the ability of Democratic voters to cast ballots.

If it became law, the bill would drastically expand early and mail-in voting, neuter restrictive state voter ID laws, make it harder to purge voter rolls while automatically registering all eligible voters and restoring voting rights to former felons. Those and other changes would most likely increase voter participation, especially by minority voters who disproportionately lean Democratic.

Senators plan to reintroduce the bill this week and Amy Klobuchar, Democrat of Minnesota and the chairwoman of the Senate committee that will advance it, has promised a hearing on March 24.

But what happens next is a matter of hot political and strategic debate centered on Democrats’ fight over the filibuster, where a handful of moderates so far appear unwilling to change or drop the tactic. All 50 Democrats probably would have to agree to alter the rules.

In an interview, Ms. Klobuchar suggested that if senators could not agree to scrap the filibuster altogether, they could try to find a compromise, potentially allowing measures on voting and elections like Senate Bill 1 to pass with a simple majority, but not other bills.

“It is so fundamental to everything else, it has to get done,” she said.

Senator Chuck Schumer, Democrat of New York and the majority leader, has been less definitive but indicated last week that he, too, may view voting rights as a unique case. “If we can get some bipartisan support, great, but if not, our caucus will meet and we will figure out how to get it done,” he said in a radio interview. “Failure is not an option.”

End Citizens United, Let America Vote and the National Democratic Redistricting Committee plan to run television and digital ads in Alaska, Arizona, Georgia, Maine and Pennsylvania, homes to several key swing senators. A later phase will target up to 15 red and blue states. The groups will also dispatch 50 paid staff members to states, including Mr. Manchin’s West Virginia.

“We almost don’t have a choice,” said Kelly Ward Burton, president of the Democratic redistricting group. “Because of what’s happening in the states, it’s not theoretical. It’s happening right before our eyes. It would be irresponsible not to do anything about this.”