In a meeting with her staff last week, Vice President Kamala Harris offered a prediction: Former President Donald J. Trump would not support a national abortion ban. Instead, she said, he would take a position that would muddy the waters on an issue that she believed could be deeply damaging for his campaign.

We need to make him own this, she told her aides.

Days later, as rumors circulated that a court ruling was coming on Arizona’s abortion ban, Ms. Harris instructed that an event in Tucson about student loans should instead focus on abortion rights, according to three Democratic officials familiar with the matter, who spoke on the condition of anonymity to discuss the internal deliberations.

On Tuesday, Arizona’s top court upheld an 1864 law that bans nearly all abortions. And on Friday, before more than 100 abortion rights activists and supporters, Ms. Harris plans to deliver a simple message: Blame Donald Trump.

From campaigns for state legislatures to the race for the White House, Democrats have unified around a central message of protecting what remains of abortion access in the United States, along with the availability of long-established reproductive health measures like contraception and fertility treatments.

The Democratic effort underscores how the 2022 Supreme Court decision ending federal abortion rights remade American politics. Four years ago, Joseph R. Biden Jr. rarely mentioned abortion rights in his general-election campaign, fearing the issue could alienate moderate voters and would not sufficiently energize his base. Now, after the fall of Roe v. Wade, abortion rights are a centerpiece of his re-election bid, the first time that an American presidential campaign has focused so intensely on women’s reproductive health.

After largely abandoning an effort to brand economic progress under the banner of Bidenomics, the president’s team has found a simpler, easier-to-understand slogan to use wherever states are restricting abortion.

“Donald Trump did this,” reads the closing shot of one of the campaign’s new advertisements about abortion.

That message, Democrats say, has been supercharged by the Arizona abortion decision. The state is only the most prominent of dozens where abortion is likely to remain front and center in November, between continued bans on the procedure, a steady drumbeat of legal rulings and painful personal stories of women affected by the restrictions, and ballot measures asking voters whether to expand rights and access.

“The more and more we see these examples, the more and more people are like: ‘Oh God, that could happen to my family. That could happen to someone I love,’” said Jennifer O’Malley Dillon, the chairwoman of Mr. Biden’s campaign. “We believe now when fundamental rights are taken away, it is not an issue people are going to forget.”

This week, Democrats have rallied around abortion rights in races from coast to coast. In Florida, former Representative Debbie Mucarsel-Powell, who is running for the Senate, began a “Florida Freedom Tour” after a decision by the Florida Supreme Court last week allowing a six-week abortion ban. In North Carolina, two women who experienced life-threatening complications after being denied abortions in their home states appeared at Biden campaign events.

Spanish-language signs erected in Phoenix and Tempe blamed Mr. Trump for the Arizona ban, and billboards in swing House districts from California to Texas accused Republicans of voting against treatments like in vitro fertilization. And in Arizona, the Biden campaign announced a “seven-figure investment” in ads focused on reproductive rights.

Much more is scheduled for the coming weeks. The Biden campaign is sketching out plans to campaign around notable — and some far less known — anniversaries over the next two months.

In May, it plans to mark the leak of a draft of the Supreme Court decision overturning Roe and the anniversary of a Nebraska ban on abortion at 12 weeks. June will bring the anniversaries of the 1965 Supreme Court decision in Griswold v. Connecticut, which legalized contraception for married couples, and of the ruling in Dobbs v. Jackson Women’s Health Organization that ended a constitutional right to abortion.

Biden campaign aides believe the issue could sway the presidential race in their favor not only in Arizona but also in North Carolina, which a Democrat last won in 2008. Even Florida could possibly be in play, they suggest, despite its recent shift to the right.

Abortion bans in places like Florida could have national ramifications, Biden campaign aides say. Florida and Arizona are not perceived to be as socially conservative as some of the Southern states that enacted bans on the procedure before the Supreme Court ruling, these aides argue, and their tightening restrictions will help illustrate the widespread impact of the court’s decision.

“Folks are keenly aware that it may be Arizona today, but in an election or two, it could come to your neighborhood,” said Lt. Gov. Austin Davis of Pennsylvania, a Democrat. “It is very much something that I hear on the road and that people come up and talk about.”

Not everyone agrees: Some within the Biden campaign worry that focusing on abortion could lead it to neglect other issues on which the president is struggling more for approval, including inflation, immigration and — this week — student loan debt.

Molly Murphy, a Biden pollster, said abortion rights were particularly motivating for younger voters, whom Mr. Biden has struggled to energize. But she said the issue resonated far beyond them, reaching much of the party’s voting base, including white women without college degrees, Latino women and suburban swing voters.

“I think we actually can’t talk about it enough,” she said. “I’ve actually not seen any group where it just falls flat.”

Polls have shown that a broad majority of voters believe abortion should be entirely or mostly legal and that more voters trust Mr. Biden than Mr. Trump on the issue. Twelve percent of voters in a recent survey by KFF, a nonprofit group focused on health policy, said abortion was the “most important issue” in their 2024 vote. That is a significant shift from 2020, when a larger share of self-described “pro-life” voters were more likely to say the issue was important to their vote than self-described “pro-choice” voters.

On Wednesday, Mr. Trump distanced himself from the Arizona law and speculated that Florida’s six-week ban was “probably, maybe going to change.” He continued to defend the position he had taken in a video statement on Monday, when he said that abortion laws should be left to the states.

Yet Democrats believe Mr. Trump will not be able to outrun blame for appointing the three Supreme Court justices who helped overturn Roe — a ruling he often highlights as a major accomplishment of his presidency. Democrats are also leveraging this strategy against other Republican candidates by pointing to their past support for legislation that would curtail or even eradicate abortion rights.

“It’s gone from an abstract concern that women might lose their right to make their own health care decisions to reality” that they have already lost it, said Josh Stein, the Democratic nominee for governor in North Carolina, which enacted a 12-week abortion ban last year. “When you compound it with the fact that we are now the southernmost state in which abortion remains lawful, it becomes all the more concerning.”

The Democratic Congressional Campaign Committee has identified 18 competitive races in states where measures expanding abortion rights are likely to appear on the ballot in November. There also are at least five competitive Senate races in states where advocates are working to place abortion questions on the November ballot — including Florida, where Mr. Trump lives. On Wednesday, he dodged a question about how he would vote on the issue.

“Democrats can run on a unifying message from state legislative races to the Senate to the presidential campaign,” said Ben Wikler, the chairman of the Democratic Party of Wisconsin, who helped liberals win a critical State Supreme Court election last year. “It creates the possibility of a surround-sound campaign.”

Many Democrats believe their most powerful message comes from the women directly affected by the state bans. Democratic strategists from the Biden campaign and for congressional candidates anticipate featuring more accounts of women delivering heart-rending accounts of losing their pregnancies and facing dire medical consequences when they were denied abortion care.

Even some Democratic candidates have begun sharing stories about their own abortions that would have been considered too politically charged even just two years ago. On Thursday, Lucia Báez-Geller, a Democrat running for Congress in a South Florida district held by a Republican, wrote about her decision to end a nonviable pregnancy at 12 weeks in an opinion essay published in The Miami Herald. Under the six-week ban, which is expected to go into effect by May 1, such a procedure would become harder, if not impossible, to receive.

“There is definitely heightened attention around this, and I just feel that my story is one of many,” Ms. Báez-Geller said in an interview. “And I think my story is going to pale in comparison to the stories that we’re going to hear when this ban goes into effect.”

Michael Gold contributed reporting.