WASHINGTON (AP) — Congressional bargainers should reach a bipartisan deal on revamping policing procedures by early summer or abandon the effort, Republicans said Wednesday, a day after George Floyd's family used visits to the White House and the Capitol to prod lawmakers to act.

"I think it's June or bust," lead GOP bargainer Sen. Tim Scott of South Carolina told reporters, the day after the anniversary of Floyd's slaying at the hands of Minneapolis police. "We've got three weeks in June to get this done."

"I think if it's going to happen, it'll happen before the July break," said Sen. Lindsey Graham, Scott's fellow South Carolina Republican and another negotiator.

Neither senator explained why they'd targeted the next few weeks as pivotal in talks that became serious in April but have produced no tangible product. But historically, it gets harder for Congress to resolve controversial issues as an election year approaches and each party seeks issues to use in upcoming campaigns. Republicans hope to win House and perhaps Senate control in the 2022 elections.

"I hope it's not being considered an ultimatum," said Hilary O. Shelton, a senior vice president of the NAACP and director of the organization's Washington office. "I hope it's to push their fellow Republicans and say, 'Let's take care of this.'"

Floyd's killing triggered the country's most widespread racial justice demonstrations in years. The Democratic-run House approved legislation in March exposing individual police officers to civil suits, banning chokeholds and establishing a national registry of misconduct by officers, but the measure has stalled in the Senate as Republicans have sought more moderate steps.

Aides to the top two Democratic bargainers, Sen. Cory Booker of New Jersey and California Rep. Karen Bass, did not immediately provide comments about the Republicans' remarks.

Momentum for action surged last month after former Minneapolis officer Derek Chauvin was convicted in Floyd's killing and President Joe Biden used a nationally televised address to urge action on legislation by the anniversary of Floyd's death. Floyd's relatives spent Tuesday afternoon with Biden and also visited members of Congress, including House Speaker Nancy Pelosi, D-Calif.

Both sides' bargainers have consistently expressed optimism about reaching a deal, with Scott saying Wednesday, "We're doing our best. We're making progress."

Yet the talks have been a slog with the key dispute over qualified immunity, a legal doctrine that usually protects individual officers from lawsuits. Democrats have wanted to eliminate that shield, while Republicans want to retain immunity for officers but allow police agencies to be liable.

The standoff showcases the problem of finding middle ground on an issue on which the two parties' core voters — Democrats' voters of color and progressives, and Republicans' conservatives — have diametrically opposed views.

Opposing interest groups underscored those differences in interviews Wednesday.

"We want qualified immunity to stand," James Pasco, executive director of the Fraternal Order of Police, the huge police organization, said Wednesday.

"We want to see an end to qualified immunity," and the bill "won't be meaningful police reform without that," said Aamra Ahmad, senior policy counsel at the American Civil Liberties Union.

The Senate begins a recess after this week and returns June 7, while the full House is already gone until June 14.