Sen. John McCain, a leading proponent of a compromise to head off the Senate's so-called “nuclear option,” suggested Monday evening that there was progress in talks between the two parties.

“There might have been a good meeting between leaders,” McCain told reporters, referring to a get together earlier Monday between Senate Majority Leader Harry Reid, D-Nev., and Senate Minority Leader Mitch McConnell, R-Ky.

Walking into a rare Republican-Democrat Senate conference meeting, McCain said senators would discuss a proposed compromise that could defuse the situation, and that the compromise had already received the support of a number of senators.

“I think it’s very important that we give those proposals — which are supported by a number of Republicans — at least the consideration of our colleagues on both sides of the aisle,” McCain said, adding that Democrats are aware of the proposal and that “many are supportive of it.”

The Arizona Republican declined to provide details about the proposal.

“I’ve been in conversations with the White House about it, they’d like to see it resolved as well. They know that it’s largely a Senate issue,” he said.

Reid has been threatening to curb the use of the filibuster, which Republicans have been using to block President Obama's nominees. Reid said he'd change the rule so that a simple majority would be enough to advance nominees, instead of the current 60-vote threshold. That would effectively allow Democrats, who control 54 seats, to advance those executive-branch nominees without Republicans.