Washington (CNN) A procedural sneak attack by a pair of Republican senators has thrown a monkey wrench into the debate over the Iran bill as the two critics of a nuclear deal with Iran insist they get votes on their amendments to toughen the legislation.

Their effort has the potential to doom the bill altogether. Republican leaders scrambled in response to find a path forward to preserve it.

The move threatens a careful effort to protect the bill from what supporters consider "poison pill" amendments that would dramatically alter the bill and lead to a presidential veto. If that happened, Congress would be cut out of any role in approving the still emerging agreement with Iran.

"I have said time and time again, the Senate needs to vote on the merits of the agreement," a frustrated Sen. Tom Cotton, R-Arkansas, said on the floor. "We have been consistently blocked from bringing up these amendments for votes."

With that, the newly minted senator exploited a procedural loophole that could force votes on an amendment he is proposing, related to Iran's nuclear facilities, and an amendment from Sen. Marco Rubio, R-Florida, to make a nuclear deal contingent on Iran recognizing Israel's right to exist.

The senators are insisting the amendments be approved on a simple majority vote, instead of the 60 votes typically required on significant measures, meaning they will be that much easier to pass.

Adding to the dramatic nature of the unexpected floor procedure, Rubio, a 2016 presidential candidate, was the presiding officer in the Senate at the time.

Cotton denied the amendments were designed to kill the bill and instead described them as "vitamin pills."

"They're designed to strengthen this legislation and strengthen the U.S. negotiating position," he said.

Cotton accused other senators of being afraid to take tough votes.

"If you don't want to vote, you shouldn't have come to the Senate. If you're in the Senate and you don't want to vote, you should leave," Cotton said.

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Stunned bill managers immediately recognized the ramifications of the move by their junior colleagues.

"I sense the context of this debate has just changed," said Sen. Bob Corker, R-Tennessee, the chairman of the Foreign Relations Committee, who was visibly miffed.

"That's every member's right to take whatever action they want to take, but I want to tell you, those of us who want to get this bill to the finish line, it gets a little frustrating," said Sen. Ben Cardin of Maryland, the top Democrat on the Foreign Relations Committee.

Republican leaders huddled Thursday afternoon in the office of Senate Majority Leader Mitch McConnell as they considered their options. No action was expected before next week.

"Right now we're a little balled up," said Sen. John Cornyn of Texas, the second-ranking Republican. "It's going to take a little while for everybody to cool down, keep talking and come up with a path forward."

GOP leaders recognize that the two amendments might pass, likely leading to a presidential veto. Few senators want to vote against requiring Iran to recognize Israel, for instance. That's why leadership has tried to stave off votes on such hot-button amendments until they felt comfortable the proposals could be defeated, with both Democrats and Republicans walking the political plank together to vote them down.

McConnell's only choice may be to move to end debate on the Iran bill altogether and forgo any more votes on amendments, including the Cotton and Rubio proposals. But doing so runs the risk of upsetting Republican senators who have a long list of amendments -- 67 as of Thursday -- they want to vote on. If McConnell can't get the 60 votes he needs to end debate, the bill could be doomed.

After Cotton's procedural move, GOP leaders temporarily set the Iran bill aside to prevent him from forcing an immediate vote on the amendments he filed. When the Senate returns to work Monday, McConnell will need to announce what his next steps will be. A final vote on the bill was expected by Tuesday but the actions on the floor Thursday may push that back.