For Democrats, the only way to break their voting rights legislation free of Republican opposition is by changing the Senate’s filibuster rules — an institution-shaking step that so far remains out of reach. But while the filibuster is proving hard to kill, it has been wounded.

The unanimous Republican refusal to allow the Senate to open a debate sought by every Democrat on the expansive elections and ethics measure — coupled with the recent filibuster of other legislation with bipartisan support — has armed opponents with fresh evidence of how the tactic can be employed to give the minority veto power over the majority.

Democrats and activists say the increasing Republican reliance on the filibuster will only intensify calls to jettison it and potentially bring about critical mass for a rules change as Democrats remain determined to pass some form of the elections measure and other parts of their agenda opposed by Republicans.

“I think as people see them stopping more things, minds might change,” Senator Amy Klobuchar, Democrat of Minnesota and one of the chief sponsors of the voting bill, said on Wednesday.

Ms. Klobuchar, who leads the Rules Committee, is planning to conduct a field hearing on voting rights in Georgia to build public support for the legislation, choosing a state where Republican lawmakers have put in place restrictive voting rules after sustaining election losses.

The White House, which has been criticized for not engaging aggressively enough on voting rights, is promising more from President Biden on the issue next week, though Mr. Biden, a senator for 36 years, has not explicitly endorsed eliminating the filibuster.

But to curb the power of the filibuster through a rules change, all 50 Democrats would have to agree to do so on the floor, and so far Senators Joe Manchin III of West Virginia and Kyrsten Sinema of Arizona have expressed strong public opposition to doing that. Ms. Sinema’s latest pronouncement came in a Washington Post op-ed published just before this week’s procedural vote, much to the frustration of some of her colleagues.

Other Democrats also remain reluctant to make significant changes to the filibuster, though they are much less outspoken than their two colleagues. One of them, Senator Angus King, a Maine independent who votes with Democrats and has previously voiced openness to changing the filibuster rule, said on Wednesday that doing so still felt premature.

“I don’t think we are done trying to find a solution,” Mr. King said, referring to long-shot attempts to lure Republicans to support a compromise on voting legislation. “We need to give them another chance to see how they feel about democracy.”

As they regroup, Democrats involved in shaping the voting rights measure agreed the next step was to produce a narrower version incorporating some of the changes sought by Mr. Manchin that their party could then rally around. That willingness to accept elements of Mr. Manchin’s proposal won his support on Tuesday for beginning debate on the legislation, allowing Democrats to present a unified front.

Senator Jeff Merkley, Democrat of Oregon and a chief author of the elections bill, said Democrats and Mr. Manchin could then try anew to recruit Republicans behind the revised bill — a prospect he acknowledged was unlikely to succeed.

Multiple Republicans have said they cannot see themselves backing any Democratic proposal imposing new voting rules on states. Senator Mitch McConnell, Republican of Kentucky and the minority leader, has drawn a firm line against cooperating with Democrats and most Republicans will be very reluctant to cross him, counting on Mr. Manchin and Ms. Sinema to keep their commitment not to alter the filibuster rules requiring 60 votes to proceed on legislation.

“If that fails,” Mr. Merkley said on Wednesday about new outreach to Republicans, “then the 50 of us who want to defend our Constitution, defend the right to vote, stop billionaires from buying elections have to be in a room and figure out how do we get around Mitch McConnell obstructing this.”

Though he was not specific, Senator Chuck Schumer, Democrat of New York and the majority leader, said on Tuesday after the vote that Democrats “have several serious options for how to reconsider this issue and advance legislation to combat voter suppression.”

“We will leave no stone unturned,” he said on Wednesday. “Voting rights are too important.”

But Mr. Schumer has other items on his to-do list, notably an infrastructure proposal prized by the White House that will consume much, if not all, of July, detracting from efforts to highlight both the voting rights measure and the drive to rein in the filibuster.

Pressed on how they can hope to convert Mr. Manchin and Ms. Sinema considering how strongly they have registered their opposition, Democrats and antifilibuster activists noted that Mr. Manchin only a few weeks ago had been dead set against the expansive voting rights bill. Democrats appeared to have lost his vote only to see him come forward with his own plan and join them on Tuesday.

At the same time, some Democrats who had been reluctant to tinker with the filibuster, like Senators Jon Tester of Montana and Chris Coons of Delaware, have expressed some willingness to do so now if Republicans maintain their blockade against the voting rights bill, though they have not taken a definitive stance.

“Time will tell,” Mr. Tester said on Wednesday about what his position would be if it came to a filibuster showdown.

After already investing heavily in campaigns in the news media, antifilibuster activists intend to use the coming two-week Senate recess to build more support for the voting rights bill and put pressure on Democrats to change the filibuster to enact it.

“This is going to be a huge motivating factor for grass-roots activists across the country to take this procedural loss and turn it into a legislative win,” said Meagan Hatcher-Mays, the director of democracy policy for the progressive group Indivisible, one of several organizations planning events while senators are back home.

Proponents of the change in the chamber signaled they were ready to take a more active stance trying to persuade their colleagues. In a forceful speech on the Senate floor Wednesday evening, Senator Christopher S. Murphy, Democrat of Connecticut, said he felt compelled to answer Ms. Sinema’s op-ed, which argued the 60-vote threshold was crucial to promoting moderation and preserving consistency in policymaking.

“Giving Republicans a veto power over legislation when they no longer believe in the same way that Democrats do or Republicans used to in the sacredness of the vote is to risk the voluntary destruction of our democracy,” Mr. Murphy said. “Consistency has merit, it does. But in this business it is often put on an unhealthy pedestal.”

Past confrontations have shown that building to significant changes in Senate rules can take some time. In 2013, Harry Reid, then the Senate Democratic leader, spent months making the case on the Senate floor that Republicans led by Mr. McConnell were unfairly using the filibuster to impede President Barack Obama from filling important judicial vacancies with highly qualified nominees.

For most of that time, Mr. Reid appeared to lack the support to institute a rules change with Democratic votes. But by November 2013, most Senate Democrats had had enough and voted to eliminate the 60-vote threshold to advance most executive branch nominees over strenuous Republican objections.

Mr. Reid, watching from afar in Nevada, said he believed something similar would eventually happen when Democratic frustration with Republican filibusters boiled over.

“The filibuster is on its way out,” Mr. Reid said in an interview. “There is no question in my mind that the filibuster is going to be a thing of the past shortly. You can’t have a democracy that takes 60 percent of the vote to get things done.”