As Democrats confront a presidential race against a resurgent and resilient Donald J. Trump as well as a brutally challenging Senate map, they believe they have an increasingly powerful political weapon: ballot measures to protect abortion rights.

Two crucial presidential and Senate battlegrounds, Arizona and Nevada, are expected to put such measures directly before voters. So are other states with top Senate races, including Maryland and potentially Montana. And abortion rights measures are set or could appear on ballots in states like New York, Florida and Nebraska, where competitive contests could help determine whether Democrats win back the House.

Hopeful Democrats — and worried Republicans — are acutely aware that in all seven states where abortion has been put directly to voters since the Supreme Court overturned Roe v. Wade, the abortion rights side has won, in both red states like Ohio and Kansas as well as swing states like Michigan. Those measures have sometimes fueled surges in liberal turnout that have lifted Democratic candidates to victory, as well.

So in every state where an abortion measure is already on the 2024 ballot or could yet appear, Democratic candidates, state parties and allied groups are campaigning furiously alongside the ballot initiatives, running ads, helping pour money behind them and bringing up the measures in speech after speech.

In Arizona, where Democrats are trying to flip the Legislature, the party’s candidates have gone so far as to collect signatures for the state’s ballot measure as they knock on voters’ doors.

“When the abortion petition initiative came out, it was a no-brainer that I would carry it with me,” said Brandy Reese, a Democrat running for the Arizona House who said she had gathered dozens of signatures while campaigning. “I introduce myself as a pro-choice candidate running, and you can instantly tell in people’s body language that they’re excited to hear that.”

The wave of abortion referendums — some of which are not officially on the ballot yet but most of which have enough signatures to get there, according to organizers — is adding new unpredictability to an election season already convulsed by Mr. Trump’s criminal cases and wrenching questions about the future of the country’s democracy.

With polls showing that a majority of Americans think abortion should be legal in all or most cases, the measures could serve as a political life raft at a time when President Biden faces stubbornly low approval ratings and skepticism within his party. Democrats hope the ballot initiatives will increase turnout among core voters like suburban women, young people and African Americans.

“The ballot initiatives are well-funded and well-organized efforts,” said Christina Freundlich, a Democratic strategist. “It’s creating a tremendous sense of energy not only within the Democratic Party but with voters across the board.”

Party leaders are echoing that message.

“Momentum is on our side,” Vice President Kamala Harris said at an abortion rights event on Wednesday in Jacksonville, Fla. “Just think about it: Since Roe was overturned, every time reproductive freedom has been on the ballot, the people of America voted for freedom.”

Beyond electoral politics, the ballot initiatives regarding abortion have driven huge interest and turnout because of their direct impact on voters’ lives. In Florida, for example, a newly enforced ban on nearly all abortions in the state has cut off a critical access point to patients across the Southeast. In Arizona, lawmakers this week repealed a near-total ban on abortions — but the state is now set to enforce a 15-week ban with no exceptions for rape or incest.

Medical practitioners have also expressed concerns about facing criminal penalties under the bans.

“The fear of that is just devastating,” said Mona Mangat, board chair of the Committee to Protect Health Care, an advocacy group that is supporting ballot initiatives in several states. “It’s going to be devastating for practitioners and devastating for patients.”

Ms. Mangat said the restrictions could affect whether doctors wanted to move to those states to practice medicine or attend residency programs.

In Nevada, abortion is legal within the first 24 weeks of pregnancy. Organizers there are collecting signatures to place an amendment on the ballot that would establish a right to an abortion in the State Constitution. Key Democrats in the state, including Senator Jacky Rosen, who is facing a close re-election fight, have signed onto the petition.

Representative Dina Titus, another Nevada Democrat, said in an interview that the amendment would still motivate voters to turn out, especially young people, even without the driving force of overturning far-reaching restrictions.

“We’ll talk about it in terms of how this will really protect women,” Ms. Titus said. “And we’ll use it to attract young women and just young people generally to the polls, because they will suddenly realize something they took for granted is not going to be available.”

Republican candidates and their allies have appeared reluctant to directly campaign against ballot measures to protect abortion rights, though some G.O.P. leaders have voiced opposition. In Ohio, Gov. Mike DeWine recorded a video opposing the state’s initiative last year, and in Florida, Gov. Ron DeSantis has said the current ballot measure is too broad. “To nuke parental consent for minors is totally unacceptable,” he said at an event last month.

Some Republicans openly worry that restrictive measures like Florida’s may play into the hands of Democrats, given how abortion referendums in recent cycles have unfolded.

“Kansas and Ohio to me is what everyone should be looking at,” said Vicki Lopez, a state representative from Miami who was one of a handful of Republican legislators to vote against Florida’s six-week ban. Voters will now decide in November whether to add a right to an abortion to the State Constitution, with a question known as Amendment Four. “This will be a test.”

But Ms. Lopez added that it would be a mistake to assume that “everyone who votes for Amendment Four is actually going to then vote for Biden.”

Regardless, Democrats believe they have the advantage. In a memo last month, the Democratic Congressional Campaign Committee wrote that “reproductive freedom will remain a driving issue for voters this November” and that the group would “ensure that House Republicans’ efforts to ban abortion nationwide are top of mind as voters head to the polls.”

The D.C.C.C. said it had identified 18 competitive House seats in states where abortion measures are likely to be on the ballot. Republicans are trying to protect a slim House majority.

Money for the ballot measures has cascaded in from both major liberal groups and small donors. Some so-called dark money organizations, whose donors are not disclosed, have contributed millions, including the Open Society Policy Center, the Sixteen Thirty Fund and the Fairness Project. Other advocacy groups, like Planned Parenthood and the American Civil Liberties Union, have also contributed seven figures.

Think Big America, an abortion rights group started by Gov. J.B. Pritzker of Illinois, has spent heavily to support abortion initiatives. After Mr. Pritzker and the group combined to drop $1 million in Ohio last year, Think Big America has spent $1.25 million in Nevada and Arizona. It has also made what it called a “quick investment” of $500,000 in Montana, where the issue is not yet on the November ballot, and donated $500,000 in Florida.

“This has a power to not only turn out Democrats but also make sure that folks that are on the fence — swing voters, independents, persuadable voters — are coming over to the side that has had a longstanding belief in reproductive freedom,” said Michael Ollen, the executive director of Think Big America.

In Arizona, Gov. Katie Hobbs has directed her well-funded state political action committee, Arizona Communities United, to focus heavily on the ballot initiative.

Ms. Hobbs, who has navigated slim Republican majorities in the Legislature for the first two years of her term, has made flipping both chambers a main goal for 2024, and she views the ballot measure as a central part of that effort.

In Nevada, the Biden campaign has invited ballot initiative organizers to collect signatures at events featuring Jill Biden and Ms. Harris.

Giving a speech in the state last month, Ms. Harris thanked the signature gatherers in the audience. They responded by holding up their clipboards and cheering.

“We’re going to win this ballot initiative,” the vice president said. “And Joe Biden and I are going back to the White House.”

Patricia Mazzei contributed reporting.