“This is a moment in history where circumstances dictate the need for change,” Mr. Reid said in a speech at the liberal Center for American Progress. He suggested that the only way for Republicans to avoid the rules change was to acquiesce to straight up-or-down votes on Tuesday on seven nominees in question and stop filibustering executive nominations in the future.

“I love the Senate, but right now the Senate is broken and needs to be fixed,” he said.

Republicans expressed outrage at the proposal and promised to retaliate. But for a Senate that has increasingly found itself tied in procedural knots, the decisions at hand were potentially momentous. Republicans to the last minute were preparing offers of compromise, but Democratic leaders said they had the votes and the wherewithal to pull the trigger on the most significant change since the early 1970s in the way the Senate operates.

Although Mr. Reid insisted that the change was extremely narrow, it had the potential to be the beginning of the end of the filibuster — and to eliminate the need for supermajorities to get anything done in Congress’s upper chamber.

Mr. Reid’s position could be a bluff to gain leverage to force the nominees through. Senators John McCain of Arizona and Lamar Alexander of Tennessee, both Republicans, were in negotiations with two Democrats, Carl Levin of Michigan and Max Baucus of Montana, to find a way out. But most senators said it was now up to Senators Reid and McConnell.

“I want a solution,” Mr. Baucus said. “That’s by far better for everyone, by far.”

After the meeting, Mr. McConnell offered Democrats up-or-down votes on all seven contested nominations in exchange for a promise to drop the rule-change threat. Mr. Reid demanded a pledge not to filibuster future nominations. Both sides balked, according to aides familiar with the exchange.

Signs earlier on Monday pointed to Mr. Reid exercising a version of what has come to be known as the “nuclear option” — meaning that rather than the 67 votes usually needed to change the Senate rules, Democrats would do so with a majority, a move that could, in the short run, eviscerate what comity is left in the chamber, and, in the longer term, fundamentally change the institution.

“It’s almost hard to measure the ramifications that would emanate from such an action,” said Olympia J. Snowe, a former Republican senator from Maine who helped head off an earlier showdown over judicial nominees. “Once you go down that path, you cannot know how this will reverberate on the institution for generations.”