▶ Watch Video: Biden pushes for voting rights bills; Kevin McCarthy squares off with January 6 committee

Senator Kyrsten Sinema, who is one of two Senate Democrats known to opposes changes to Senate rules to pass voting rights legislation, is speaking on the Senate floor Thursday, ahead of President Biden’s lunchtime meeting with Senate Democrats on Capitol Hill.

Mr. Biden is pressing lawmakers to alter Senate rules to enable two voting access bills to pass with a simple majority, rather than a super majority of 60 votes, and Arizona’s Sinema and West Virginia’s Joe Manchin have openly expressed their opposition to such a change.

In a speech in Atlanta on Tuesday, the president said publicly for the first time that he supports nixing the filibuster for the voting bills. 

“I’ve been having these quiet conversations with members of Congress for the last two months. I’m tired of being quiet!” the president exclaimed.

The House on Thursday, in a 220-203 vote, passed a consolidated voting bill that would be the first step in enabling the Senate to debate voting rights changes on the floor. 

“Nothing less than our democracy is at stake,” Pelosi said Wednesday. 

Meanwhile, Republicans are warning the president and Senate Democrats against changing the Senate rules.

“This is more than just about one issue,” said Republican Senator Shelley Moore Capito of West Virginia. “This is about fundamentally changing the fabric, the fence that the Senate provides by having the filibuster in place to make sure that we don’t have the dramatic swings from administration to administration, from majority to minority, [from] Republican to Democratic, and that we keep the ship sort of going in the right direction and working together at the same time.”

CBS News’ Jack Turman and Adam Brewster contributed to this report.