WASHINGTON—In the weeks since President Biden’s agenda stalled in a bitterly divided Congress, something unusual happened on Capitol Hill: Democrats and Republicans started working together.

Already, bills to make the U.S. Postal Service more financially viable, boost U.S. competitiveness with China and ban mandatory arbitration in cases of sexual assault and harassment have picked up steam in Congress. Senators passed the arbitration bill by voice vote, sending it to the president’s desk without a single member of either...

WASHINGTON—In the weeks since President Biden’s agenda stalled in a bitterly divided Congress, something unusual happened on Capitol Hill: Democrats and Republicans started working together.

Already, bills to make the U.S. Postal Service more financially viable, boost U.S. competitiveness with China and ban mandatory arbitration in cases of sexual assault and harassment have picked up steam in Congress. Senators passed the arbitration bill by voice vote, sending it to the president’s desk without a single member of either party demanding a roll call to record yeas and nays.

Legislators also announced an agreement on a framework for legislation to fund the federal government through fiscal year 2022, and a deal to reauthorize a landmark domestic-violence bill, which lapsed in 2019.

“For those who have given up hope on the United States Senate functioning, passing important laws, working together on a bipartisan basis, take a look behind me,” said Sen. Dick Durbin (D., Ill.), flanked by a group of Democratic and Republican senators at a press conference introducing bipartisan legislation to reauthorize the Violence Against Women Act.

Some issues still face hurdles. For instance, talks on a Russian sanctions bill foundered last week in the midst of disagreements over whether sanctions should be imposed immediately, or only kick in if Russia invades Ukraine. Mr. Biden’s Supreme Court pick, expected soon, also will test the limits of bipartisanship.

Both sides, though, see more room for deals. House and Senate lawmakers are working across party lines to restrict stock trading by members of Congress. Sixteen senators from both parties are working to overhaul the 135-year-old Electoral Count Act, to clarify the vice president’s role in certifying election results and strengthen protections for election workers, among other potential updates to federal voting laws.

Democratic Sen. Joe Manchin says lawmakers are realizing they have to work together.

Photo: Tom Brenner/Reuters

This flowering of bipartisanship comes about two months after centrist Democratic Sen. Joe Manchin of West Virginia said he would oppose Mr. Biden’s roughly $2 trillion economic and climate package, effectively killing it in the 50-50 Senate with all Republicans opposed. A month later, Democrats fell short of the votes needed to change the Senate rules and pass voting-access legislation that they had called a priority. In that debate, Democrats lashed out at Republicans, with Mr. Biden at one point saying that opponents were on the side of Confederate traitors and segregationists.

Mr. Manchin said that members of Congress are finally coming to the realization that they have to work together.

“That’s the way the place was designed,” he said. “I think we oughta come back to our senses and let’s try to get something done…Republicans too need to be reaching out. We all need to give and take.”

Sen. Susan Collins (R., Maine) said she fielded an unprecedented number of calls in the past week from the White House—from top Biden adviser Steve Ricchetti, chief of staff Ron Klain and the president himself. She said Democrats have become more flexible in negotiations and willing to retreat from some red lines, a shift she tied to the party’s failure to change the filibuster rule, which requires 60 votes to advance most legislation.

Republican Sen. Susan Collins says Democrats have become more flexible since the party’s failure to change the filibuster rule.

Photo: Jim Lo Scalzo/EPA/Shutterstock

On the Violence Against Women Act, or VAWA, Democrats had for years pushed to close the “boyfriend loophole” by adding language to the bill that would have barred people convicted of crimes related to dating violence from possessing firearms. The bill’s supporters had struggled to get at least 10 Republicans to commit to voting for it as long as it contained a measure they saw as restricting gun rights, so Democrats agreed to drop the language.

“As one Democrat said to me, ‘I’m tired of letting the perfect be the enemy of the good,’ and I think that is what has happened,” Ms. Collins said.

Sen. Rob Portman (R., Ohio) also pointed to Democrats’ inability to change the filibuster rule as the reason for their renewed interest in working across the aisle in the 50-50 Senate. “Democrats finally realized they have to work with us,” he said.

Democratic senators interviewed by The Wall Street Journal denied any connection between the failed filibuster effort and the current bipartisan streak. Instead, some said, the shift is a recognition that narrower bills often have better prospects for passage.

Sen. Tim Kaine (D., Va.) said Congress tends to focus on big bills, but some Democrats are now betting that they will accomplish more if they aren’t always trying to hit home runs.

“If you’re willing to hit some doubles, and singles and triples, you can get a lot of stuff done,” he said.

President Biden said at a news conference in January that the stalled $2 trillion Build Back Better proposal would likely have to be split up to get certain pieces, such as provisions on climate, energy and early-childhood education, passed. Photo: Oliver Contreras/Sipa/Bloomberg News The Wall Street Journal Interactive Edition

Asked to comment on the legislative progress in Congress, the White House pointed to a tweet Friday by Mr. Biden in which he said that Democrats and Republicans are “proving that we can still come together to deliver important progress for the American people.”

Senators and aides from both parties caution that there are limits.

Compromise continues to be a tough sell in policy areas that were part of the Build Back Better Act, the Democrats’ package that included provisions on climate, prekindergarten and child care among other things. Democrats are reluctant to give ground on provisions that they still hope to pass under the reconciliation process, which allows certain legislation tied to the budget to advance with 51 votes.

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But Ms. Collins, who is leading talks on revising the Electoral Count Act, sees future areas of possible collaboration on a pandemic preparedness bill, workforce legislation to address the shortage of workers or the expansion of child-care development block grants.

“There’s only so long you can bottle up creative minds of legislators,” said Sen. Ben Cardin (D., Md.). “So I think this has been pent up for a while and it feels good.”

Sen. John Cornyn (R., Texas) said of the Democrats: “To be less charitable, I might say they’re desperate to be able to put some points on the scoreboard between now and the midterm election. But I’ve always believed that it’s like a Venn diagram, you know…Maybe there’s some areas of overlap.”

—Alex Leary contributed to this article.

Write to Lindsay Wise at lindsay.wise@wsj.com