The House is set to pass its own reforms Wednesday, but Lee and Paul argue that the bill does not go far enough. Paul said Wednesday that he is pushing for an amendment stating that “FISA warrants can’t be used on Americans and no information gathered in the FISA court can be used to convict an American.”

Meanwhile, Lee said he is actively trying to get enough votes to block the House bill from advancing in the Senate.

“There are a lot of procedural tools at our disposal,” the Utah Republican said. “The rules and the clock are on our side here.”

The House bill comes a week after Senate and House Republicans met with President Donald Trump and Attorney General William Barr to discuss FISA reform. At the meeting, the president made clear that he would not support a clean extension of the expiring surveillance provisions and told lawmakers to come back to him once they reach a bipartisan deal. The president has criticized FISA after authorities used it to monitor an associate of his 2016 presidential campaign.

A senior administration official said Wednesday that “there are a lot of FISA improvements in the proposal that are wins for the president and conservatives who believe FISA was significantly abused and needed major reform.” Barr is also supportive of the proposal.

The administration official said the president "remains open" but wants to ensure that all voices are heard.

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Lee said that he spoke to Trump Tuesday evening and plans to speak with the president again Wednesday to urge him to veto the bill.

“I’ve publicly and privately suggested that,” he said. “When you have broad laws that give too much power to government officials who are answerable to no one and who are able to undertake a secret process through a secret court where no one ever has a chance to appeal or even quash a subpoena, you’re going to have problems.”

GOP Senate leaders were cautious Wednesday when discussing how the Senate would proceed. Senate Majority Leader Mitch McConnell (R-Ky.) has made clear he supports an extension to the FISA provisions.

“The House is going to take it up, let’s see how the vote is over there,” said Senate Majority Whip John Thune (R-S.D.). “I think Rand would obviously like a vote and so we’ll see what can be done, I think a lot of it will depend on whether or not there’s ... a process that gets us to a result.”

Senate Intelligence Committee Chairman Richard Burr (R-N.C.) said he had not yet read the House bill, but acknowledged that there was no backup plan before the key provisions expire.

Sen. Roy Blunt (R-Mo.), another member of GOP leadership appeared skeptical Wednesday morning about lawmakers easily passing the House FISA bill.

“I think there’s a possibility that without cooperation this could lapse for a few days,” he said. “I’m not optimistic that there will be full cooperation.”

Andrew Desiderio contributed to this report.

