For younger voters, who polls have shown to be cool to Mr. Biden and his party, the package contains the most sweeping efforts to address climate change in American history. For older voters, the deal includes popular measures sought for decades by Democrats to rein in the price of prescription drugs for seniors on Medicare. And for both the Democratic base and independents, the deal cuts against the Republican argument that a Democratic-controlled Washington is a morass of incompetence and gridlock unfocused on issues that affect average Americans.

“It’s very significant because it shows that the Democrats care about solving problems, it shows that we can get things done and I think it starts to turn around some of the talk about Biden,” said Representative Dina Titus, a Nevada Democrat running in a competitive re-election race, alluding to angst about the president as his national approval rating has hovered around 40 percent.

Adding to the Democratic Party’s brightening outlook were the results of the Kansas referendum on abortion rights last week, when a measure that would have removed abortion protections from the Kansas Constitution was overwhelmingly defeated. It was a stark reminder of the volatile and unpredictable political impact of the Supreme Court’s overturning of Roe v. Wade.

“I can kind of feel it on the streets, that there’s some change in momentum,” Ms. Titus said.