"We got the votes to confirm Justice Ginsburg's replacement before the election," Graham said. "We are going to move forward in the committee. We're going to report the nomination out of the committee to the floor of the United States Senate so we can vote before the election. That's the constitutional process."
Republicans hold a slim three-seat majority in the Senate.have said they do not support a vote before the election, but four Republicans would have break with the party to prevent a vote from coming to the floor. Senator Mitt Romney of Utah, to vote in favor of convicting President Trump on one article of impeachment, has not yet weighed in. If the vote is split 50-50, Vice President Mike Pence would cast the tie-breaking vote.
Senator Cory Gardner, a moderate Republican from Colorado who is in a tough reelection fight, said Monday said he would vote to confirm a "qualified" nominee. Senator Lamar Alexander of Tennessee, who is retiring after this term, said something similar.
Senate Majority Leader Mitch McConnell said on Friday that there will be a vote to confirm Mr. Trump's nominee.
In 2016, the Republican majority refused to allow a confirmation vote on Merrick Garland, President Obama's pick to replace Justice Antonin Scalia, who died in February of that year. Republicans said at time that they did not believe that senators should confirm a Supreme Court nominee the same year as an election.
Despite strong words from many Republicans — including Graham — in 2016 about a vote in an election year, many have different opinions this year after Ginsburg's death. In 2018, Graham said in an interview that he would not vote to fill a vacancy in 2020 if "the primary process has started."
"If an opening comes in the last year of President Trump's term, and the primary process has started, we'll wait to the next election," Graham said.
On Monday, Graham told Sean Hannity that after, "everything changed with me." During Kavanaugh's contentious confirmation hearings, a woman testified that he had sexually assaulted her while they were in high school. Kavanaugh denied the allegation.
Democrats, meanwhile, have called for the process to be halted. Senate Minority Leader Chuck Schumer said on a call with Democrats "our number one goal must be to communicate the stakes of this Supreme Court fight to the American people," according to a source on the call.
"Let me be clear: If Leader McConnell and Senate Republicans move forward with this, then nothing is off the table for next year," Schumer said. "Nothing is off the table."
Nancy Cordes contributed to this report.