WASHINGTON — Black and progressive allies of President Biden, discouraged by dispiriting legislative losses on social spending and voting rights, said on Wednesday that they see the chance for Mr. Biden to name a replacement for Justice Stephen G. Breyer as a welcome opportunity for a shift in focus and a much-needed win.

The president urged patience as Justice Breyer worked through his announcement — “I’m happy to talk about it later,” he told reporters — but it made him just about the only Democrat in Washington who refrained from immediately drawing up lists of potential replacements based on his campaign promise to nominate a Black woman to the court.

“My first thought is just that it moves us one step closer in a long journey towards racial justice,” Representative Ro Khanna, a progressive Democrat of California, said in an interview. “It’s really about what you want America to be over the next 50 years.”

Mr. Khanna added that the vacancy could be a “galvanizing” moment for voters across the Democratic spectrum who were feeling dejected, particularly after Mr. Biden’s failure to push Democratic senators to pass voting-rights legislation.

LaTosha Brown, a co-founder of Black Voters Matter, skipped Mr. Biden’s voting rights speech in Atlanta this month, criticizing what she said was a White House effort that had come too little and too late.

But on Wednesday, Ms. Brown said she was ebullient over the prospect that Mr. Biden could make good on a different promise, one that he made to voters in South Carolina during the difficult early days of his campaign. Black women, she said, “have stood on the front lines of democracy, not just for ourselves but for others.”

Donna Brazile, the Democratic strategist, became emotional as she discussed the prospect of seeing a Black woman on the court.

“This matters because it’s another symbol — it’s public leadership,” she said. The Supreme Court, she added, “has always been perceived as the domain of white males, and once you put a Black woman in there, honey, you’ve broken up everything.”

A sea change is unlikely: The retirement of Justice Breyer, who at 83 is the court’s oldest member, will do little to shift the ideological balance of the court after its rightward shift after the Trump-era appointments of three more conservative justices.

It also may ultimately do little to motivate voters in midterm election season sure to be dominated by issues like the economy and the pandemic, which have helped to drag down Mr. Biden’s poll numbers and left his party at risk of losing control of the House and possibly the Senate in November.

Still, it is a chance for Mr. Biden to add the first woman of color to the court since Justice Sonia Sotomayor, who was nominated by President Barack Obama in 2009, and to remind those who voted for Mr. Biden that he can still make good on the promises he has made to them.

“I hope that this is a moment for all Democrats to rally around their president and move quickly to show that with power came results,” said Faiz Shakir, a close adviser to Senator Bernie Sanders of Vermont. “Especially when a lot of the legislative agenda is stalemated, this can send the message back to voters who put him in the White House; here’s tangible results from the fact that you put us in power.”

Although the makeup of the Supreme Court in the past has been an issue that has galvanized voters on the right to a far greater extent than those on the left, several strategists said recent developments — including a move by the court to take up a case that challenges Roe v. Wade, the landmark ruling that established a constitutional right to abortion — had changed that.

Fatima Goss Graves, president and chief executive of the National Women’s Law Center, said that a refusal by the court to block a Texas law that would prohibit most abortions also awakened voters to what was at stake. “People expect the court to be an institution that not only interprets our laws but that actually reflects this country,” she said.

The opportunity for Mr. Biden to appoint his first justice gives the Democratic Party the “opportunity to really elevate what the conservative takeover of the court means for real people,” said John Podesta, a former chief of staff to Mr. Obama, alluding to the likelihood that the court this year will overturn or substantially scale back the right to abortion established nearly half a century ago in Roe v. Wade.

“They didn’t think reproductive rights were actually going to be taken away,” he added. “Now they know it’s true. And it’s true across a range of issues.”

Democratic voters, others say, have been alarmed by what they see as an all-out effort by Republicans, led by Senator Mitch McConnell of Kentucky, to shift the balance of court at all costs, beginning with scuttling the nomination of Mr. Obama’s third Supreme Court nominee, Merrick B. Garland. The bitter confirmation process of Justice Brett M. Kavanaugh and the installation of Justice Amy Coney Barrett just days before the 2020 presidential election, have only further concerned them.

“Enormous scar tissue was left as a result of that decision by Leader McConnell,” Valerie Jarrett, a former senior adviser to Mr. Obama, said in an interview, recalling the Garland nomination. “I do think, in light of the landmark decisions that are now up for review and the controversy around Donald Trump’s appointments, that people generally are paying very close attention to the composition of the court.”

Geoff Garin, a Democratic pollster, said that the coming confirmation process could also be a powerful reminder to voters of the importance of keeping a Democratic majority in the Senate.

“Democratic voters are painfully aware of what would happen if McConnell were in charge of the Senate if there were a nomination,” Mr. Garin said. “At a time when some Democratic voters are feeling unsure of what the benefit of a Democratic majority is, having a Supreme Court fight makes the importance crystal clear to voters.”

Senate Democrats have promised a quick confirmation process. The list of possible replacements includes women who have already weathered the Senate confirmation process, including Judge Ketanji Brown Jackson, who successfully did so last year, when Mr. Biden elevated her from the Federal District Court in the District of Columbia to the powerful U.S. Court of Appeals for the D.C. Circuit.

Two other options include Justice Leondra R. Kruger of the California Supreme Court and J. Michelle Childs, whom Mr. Biden said he would nominate for federal appeals court for the District of Columbia Circuit, a frequent staging ground for potential Supreme Court justices.

“When I think about the many Black women attorneys who have such rich and deep experience who the country basically have not yet met,” said Ms. Goss Graves, of the National Women’s Law Center, “I am excited for the country to be introduced to the long list.”

Republicans were quickly dismissive. “Replacing one liberal with another liberal, that’s just running in place,” said Senator John Barrasso, Republican of Wyoming.

But several activists said this ignored the reality that appointing a Black woman to the highest court in the land would be a historic first, one that could help Mr. Biden win back trust with a number of voters who helped him win the election. “It could energize people that have been in many ways demoralized around voting,” the Rev. Al Sharpton said.