Senate Democrats are scrambling to map out their next moves on voting rights as the clock ticks toward a key deadline this month, with Majority Leader Charles E. Schumer (N.Y.) eyeing a potential second vote on election legislation in the coming days.

Democrats’ quest for legislation that would override restrictive state voting laws, including those passed by Republican legislatures in recent months, has been eclipsed on Capitol Hill in recent weeks by the push for a bipartisan infrastructure deal and the debate over the remainder of President Biden’s vast economic agenda.

But key senators have continued to work behind the scenes after Republicans blocked Democrats’ marquee elections-and-ethics bill, the For the People Act, in late June in hopes of writing a narrower bill that could consolidate Democratic support and apply new pressure on Republicans to compromise.

That effort has yet to produce a final product, but multiple Democrats who spoke on the condition of anonymity to candidly describe the talks said they expect an agreement within days. That, they said, could set up a new vote in the Senate before the summer recess likely begins next week.

The negotiations continued Wednesday in an evening meeting that involved Schumer and several other senators. Two Democrats familiar with the negotiations said Schumer has signaled that additional votes on voting rights are likely before the Senate breaks for the summer.

Schumer spokesman Justin Goodman declined to comment on the talks but pointed to a July 22 interview in which Schumer told radio host Joe Madison that he would “bring up voting rights and democracy for future votes on the floor, and we’re going to keep at it until we get it done.”

The Senate is expected to pass the infrastructure bill as soon as this weekend, then immediately turn to budget legislation that would tee up Biden’s multitrillion-dollar economic package. Voting rights legislation could be added to the agenda after that, though debate is likely to be minimal before senators vote and leave until September.

“We’re continuing to make progress,” said Sen. Raphael G. Warnock (D-Ga.), who is among the Democrats negotiating the package and declined to comment on the details of the talks. “We are all working together to get voting rights done.”

Yet there is no signal that Republicans will be any more willing to join Democrats in advancing the revised legislation — meaning that any vote will constitute a further exercise in persuading Democratic holdouts to eliminate or modify the filibuster, the supermajority rule that allows a united minority to block legislation.

“I’m not for the federal government taking over elections at the state and local level, and I think that’s the fundamental concern,” Sen. John Cornyn (R-Tex.) said Thursday, predicting united GOP opposition.

Bearing down on the Democrats are the preparations for the 2022 midterm elections — including the drawing of new House district lines based on the results of the 2020 Census. That has sparked warnings from advocates of stronger federal voting rights laws, who say Congress needs to act this month to guarantee that any new protections can be implemented for 2022.

Democrats, for instance, are determined to curb partisan state redistricting, which could allow Republicans to net enough seats to reclaim the House majority, but several key states are readying to draw lines at a breakneck pace once the Census Bureau issues detailed population data on Aug. 12.

“We’re acutely conscious of the fact that there has to be plenty of time . . . for election clerks and for secretaries of state to lay down the foundation for implementing these reforms,” Sen. Jeff Merkley (D-Ore.) said. “We’re very aware that action has to be extremely urgent when we return.”

Despite the lack of final agreement, Democrats and allied advocacy groups are eager to show progress and return Capitol Hill’s attention to voting rights.

Toward that end, Sen. Amy Klobuchar (D-Minn.) introduced legislation Thursday that would federally ban attempts to threaten or intimidate election officials and to strengthen security requirements for ballots and other election records.

The bill, likely to be included in the revised package being finalized, would appear to outlaw some of the actions that President Donald Trump took in the wake of the 2020 presidential elections. Those include personal calls to Georgia Secretary of State Brad Raffensperger and an investigator in Raffensperger’s office in which Trump told the officials to find fraud that could swing the state’s electoral votes. The ballot security requirements, meanwhile, could make it more difficult to conduct partisan audits, such as the effort underway in Arizona.

Klobuchar, who has played a leading role in the voting rights push as chairwoman of the Senate Rules and Administration Committee, said in a statement that the new bill is aimed at a “barrage of threats and abusive behaviors by those seeking to overturn election results.”

“We need to respond to these threats head on to protect those who are on the front lines defending our democracy,” she said.

Meanwhile, a well-financed liberal advocacy group — End Citizens United — is launching a million-dollar advertising campaign calling on Democrats to pass voting rights legislation immediately — and to revise the Senate’s filibuster rule to do it.

The filibuster allows a minority of 41 senators to block the advancement of most legislation, and Republicans were able to use the rule to scuttle the For the People Act in June. While Senate Democrats have taken advantage of the rule to block GOP priorities during their time in the minority, some are now pushing for its elimination or revision to allow voting rights protections to advance with a simple-majority vote.

But key Democrats, including Sens. Joe Manchin III (W.Va.) and Kyrsten Sinema (Ariz.) have defended the filibuster, and Biden has shown little desire to press for a rules change.

The End Citizens United ad is set to run for two weeks starting Tuesday on national programs, as well as targeted buys in Pennsylvania, Michigan and Wisconsin — swing states that Biden won with significant Black populations.

The ad calls for the passage of both voting rights bills, and it is unique among recent televised advocacy efforts in targeting Biden — not individual senators — in calling for the end of the filibuster.

The centerpiece of the ad involves 1963 comments from the Rev. Martin Luther King Jr., juxtaposed with images from the civil rights movement, condemning “senators who will use the filibuster to keep the majority of people from even voting” for blocking the passage of civil rights legislation.

“President Biden, please tell the Senate: Reform the filibuster,” the ad concludes. “Everything is at stake.”

Tiffany Muller, End Citizens United’s executive director, said “time is running out” for action and criticized the suggestion from some Democrats that voter mobilization can effectively counter the state restrictions.

“We can’t out-organize this,” she said. “We know that we need these federal protections in place. And so we feel like it’s time to up the pressure even more. . . . What we need is everyone, including the president, putting the same political muscle into getting this bill passed as what we’ve seen with infrastructure — holding events across the country, using Cabinet secretaries, having daily meetings with folks on the Hill about the legislation and the path to passage.

According to Democrats familiar with the talks, several key issues remain unresolved with the revised bill, including the mandatory voter ID requirements and public financing of congressional elections. The negotiators, Democrats said, are also undecided on whether to issue legislative text ahead of the break or instead issue an outline of what the legislation would include.

But one of the Democrats involved said there is an emerging consensus that another vote is needed to “set the stage” for further action in the fall — and push those resisting filibuster revisions to change their views.

“We’ve got a bill that 50 Democrats can agree on,” the person said. “It’s moved significantly in the direction of some of the provisions Republicans wanted. So go out and see if you can get Republicans to join us, and that will set the stage for when we come back.”