Sen. Mike Lee, R-Utah, continued to push for the Senate to pass the SAVE America Act.

In a TV interview Sunday, Lee called on his colleagues to do the "hard work" necessary to pass the SAVE America Act, which would require proof of citizenship to register to vote.

Lee touted the bill, saying it makes "it easy to vote, hard to cheat." 

"The Senate needs to be willing to do the hard work to make sure that that happens," Lee said.

"If we put it on the floor tomorrow and we announce that we're going to debate it until it passes, I'm confident that we can get there," Lee added.

While the bill passed the GOP-controlled House, it has stalled in the Senate because Republicans lack the 60 votes needed to overcome a Democrat filibuster.

But Lee remains undeterred, saying there are multiple ways to secure passage of the legislation.

"We're 10 votes shy of cloture, of forcing debate to a close; that doesn't mean that we couldn't pass it," Lee said.

"There are a couple ways to get there. One would be nuking the filibuster; as you pointed out, that appears not likely to happen," Lee added. "But the other way is to exhaust the other side, to continue to debate the bill until it passes."

Lee said the SAVE America Act is worth tying up the Senate floor until it is passed.

"We haven't tried what I believe it takes to get the SAVE America Act passed, which is to put it on the floor and to say we're going to debate this for weeks," Lee said.

"And we'll stay through weekends. We'll stay through previously scheduled recesses if necessary, but we're going to stay on this bill until it passes," Lee added.

President Donald Trump has made passage of the SAVE America Act one of his top priorities, vowing not to sign legislation reauthorizing Section 702 of the Foreign Intelligence Surveillance Act, which allows the warrantless collection of communications involving targeted foreigners located outside the U.S., until SAVE passes.