G.O.P. Scrambles to Respond to Public Demands for Police Overhaul

Republicans are also feeling pressure from a newly confident Democratic Party, which believes it has finally reclaimed ground when it comes to public trust around law and safety. Many of them fear that Democrats will brand any compromise that Republicans would be willing to accept as insufficient, and use the issue instead to score political points in an election year that appears increasingly promising for them.

In a brief interview on Tuesday, Speaker Nancy Pelosi said she saw no reason that Republicans should not support the Democrats’ bill if the public does. She compared the political dynamic with gun safety, where Republicans have seen public opinion surpass their appetite to legislate and the difference undermine them electorally in suburban America.

“I hope it is better than what they did on their own proposal with gun safety,” she said of whatever Mr. McConnell and Mr. Scott were putting together.

On Wednesday, the Democratic-led House Judiciary Committee will hold a hearing examining the changes proposed in their legislation. Philonise Floyd, the brother of George Floyd, will testify. A House vote is expected by the end of the month.

With pressure mounting, a number of Senate Republicans indicated during a private luncheon on Tuesday that they were eager to pass some sort of overhaul package. Senator Tom Cotton, Republican of Arkansas, who has recently made the case for the military to be brought in amid the protests, stood to urge his colleagues to be “sensitive” to the experience that black men have with law enforcement and called on lawmakers to change that relationship, according to two people familiar with the private comments.

Senator Bill Cassidy, Republican of Louisiana, also pressed for his party to take action.

“Judging by emails, phone calls to the office and conversations, there’s a great sense of sorrow regarding George Floyd’s death,” Mr. Cassidy said. “One law enforcement officer told me that big departments cannot reform from within. They need an external influence for accountability.”

Mr. Scott shared a preliminary proposal during the lunch, but lawmakers said it would continue to evolve.