“Anger becomes action when it’s directly tied to a moment, and the moment now is the election on Nov. 8,” said Stacey Abrams, a Democratic state representative from Georgia and the House minority leader there, adding that Mr. Scalia’s death meant that this presidential campaign could no longer be construed as a mere “thought exercise.”

For Hillary Clinton, who is increasingly relying on nonwhite voters to ensure her success against Senator Bernie Sanders of Vermont, the court issue could be especially crucial. Should she defeat Mr. Sanders, who has electrified many liberals, she will need a motivating issue to bring Mr. Obama’s loyalists to the polls. She moved swiftly Tuesday to tap into the anger of blacks over the opposition of Senate Republicans to Mr. Obama’s naming a replacement for Justice Scalia.

“Now the Republicans say they’ll reject anyone President Obama nominates no matter how qualified,” Mrs. Clinton said in remarks before a predominantly black audience in Harlem. “Some are even saying he doesn’t have the right to nominate anyone! As if somehow he’s not the real president.”

Doing so, Mrs. Clinton added, is in keeping with a longstanding pattern of mistreatment.

“They demonize President Obama and encourage the ugliest impulses of the paranoid fringe,” she said. “This kind of hatred and bigotry has no place in our politics or our country.”

Republicans are especially sensitive about the notion that they are diminishing Mr. Obama because of his race, and spokesmen for several Republican senators, including Mr. McConnell and Senator Tim Scott of South Carolina, declined to comment or would not make the senators available for comment.

The suggestion that racism is playing a role angers Mr. McConnell’s friends, who point out that his formative political experience was working for a Republican senator who supported civil rights, that he helped override President Ronald Reagan’s veto of sanctions against the apartheid government in South Africa and that he is married to an Asian-American woman.