▶ Watch Video: Biden pushes voting rights bill on Capitol Hill President Biden met Thursday afternoon with Senate Democrats, saying “as long as I’m in the White House … I’m going to be fighting for these bills,” hours after Senator Kyrsten Sinema, one of two Senate Democrats known to oppose changes to Senate rules, said Thursday on the Senate floor that she will not change her position. Her remarks come moments ahead of Mr. Biden’s lunchtime meeting with Senate Democrats in which he encouraged lawmakers to overhaul Senate rules to allow the voting bills to pass with a simple majority, rather than 60 votes. Following that meeting, the president told reporters he hopes they can pass the legislation but he’s “not certain” they can. “Like every other major civil rights bill that came along, if we missed the first time, we could come back and try it a second time. We missed this time. We missed this time,” he said. “… I don’t know that we can get it done, but I know one thing: As long as I have a breath in me, as long as I am in the White House, as long as I’m engaged at all, I’m gonna’ be fighting to change the way these legislatures have moved.” Arizona’s Sinema and West Virginia’s Joe Manchin have repeatedly and openly expressed their opposition to such a change. National Democrats are trying to pass the Freedom to Vote Act, which would establish national election standards, and the John Lewis Voting Rights Advancement Act, which would reinstate a core provision of the Voting Rights Act. Manchin and Sinema met with Mr. Biden Thursday night. After the session, a White House official said only that, “The President hosted Senator Manchin and Senator Sinema at the White House tonight for a candid and respectful exchange of views about voting rights.” Sinema said she continues to support the legislation and emphasized the need to prohibit states from restricting voting access, but said such change cannot come at the cost of further division. “While I continue to support these bills, I will not support separate actions that worsen the underlying disease of division afflicting our country,” Sinema said on the Senate floor. “There’s no need for me to restate my longstanding support for the 60 vote threshold to pass legislation. And there’s no need for me to restate its role protecting our country from wild reversals in federal policy.” Eliminating the 60-rule vote on a party line “will not guarantee that we prevent demagogues from winning office,” she said. “Eliminating the 60-vote threshold will simply guarantee that we lose a critical tool that we need to safeguard our democracy from threats in the years to come,” she added. The senator from Arizona expressed frustration with both Republicans in blocking the voting legislation, and Democrats in trying to alter Senate rules. Following the meeting, the president said he hopes they can pass the legislation, but isn’t sure. “I hope we can get this done,” he told reporters. “But I’m not sure.” Manchin said the president gave a “wonderful speech,” while Senate Majority Leader Chuck Schumer said Senate Democrats are “going to do everything we can to pass these two bills.” 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.” White House press secretary Jen Psaki didn’t say whether the White House has identified more executive actions the president can and plans to take, pointing out the president signed an executive order early on in his presidency to promote voting rights. Psaki acknowledged that it can be difficult to get things done with a small majority in the Senate. “The president’s view is we’re going to keep pushing for hard things, and we’re going to keep pushing the boulders up the hill to get it done,” she said. CBS News’ Jack Turman, Fin Gomez and Adam Brewster contributed to this report.