That didn't sit well with senators trying to shepherd the bill to passage without alterations that could derail it.
"I think that's probably made it harder to get more amendments because we can't move forward," said Sen. Lindsey Graham (R-S.C.), a potential presidential candidate.
Graham said that while he agreed with the substance of the Rubio's amendment — requiring Iran to acknowledge Israel’s “right to exist” -- he is not interested in changes that could cause the agreement, which took weeks of wrangling from both parties, to fall apart.
"Bottom line is: I'm focused on the outcome and holding the bipartisan coalition together," said Graham of the measure, which cleared the Senate Foreign Relations Committee earlier this month with unanimous support.
Sen. John McCain (R-Ariz.), a leading national security hawk, was staying out of it.
"In my view he's free to do whatever he wants. He's a senator," said McCain of Rubio, striking a studiously neutral posture.
Sen. Ben Cardin (Md.), the lead Democrat trying to protect the bill, which would give Congress 30 days to review a nuclear agreement with Iran, voiced frustration at the Cotton-Rubio tactic. He said the move caught him and Sen. Bob Corker (R-Tenn.), the lead Republican behind the bill, "off-guard."
"There was no notice to either one of us," said Cardin, who added that the maneuver to get straight majority votes on the amendments "takes away some of that flexibility to get more members' input. So, it makes it more complicated."
Rubio, as he has been running for president, has sought to portray himself as a staunch national security hawk. His alliance with Cotton is the latest sign that he is determined not to get outflanked by his opposition.
In just a few months in the Senate, Cotton has ruffled feathers with his blunt foreign policy tactics, most notably his open letter to Iranian leaders aimed at derailing the Obama administration's nuclear agreement.
Cotton spokeswoman Caroline Rabbitt said Cotton and Rubio have "been in communication over the last several days about the bill." Rubio spokeswoman Brooke Sammon said she was not sure of the exact time when Cotton and Rubio decided to use a procedural tactic to try to advance their amendments, but "they did it earlier today."
"The reason why the existence of Israel as a Jewish state is directly tied to this deal is simple -- we are about to turn over billions of dollars into their hands and we have every reason to believe that they will spend a significant portion of that money to destroy our strongest and most important ally in the region and one of our most important allies in the world,” Rubio said of Iran on the Senate floor Wednesday.
Graham wasn't the only potential Rubio rival to voice skepticism about his amendment. Former Florida governor Jeb Bush said Thursday, "I understand the sentiment” of the proposal, but “I don’t know if that kills the bill and you have no legislative oversight.”
The Senate is done voting for the week, punting the Iran bill into next week's business. Corker and Democrats had been working on an agreement to get votes for some amendments. But speaking on the Senate floor after Cotton, Corker said the Cotton-Rubio maneuver "changed" the "context" of the proceedings.
In particular, Rubio's Israel amendment has proved tricky, especially for Democrats, since a vote on it would force them to choose between voicing support for Israel or protecting an agreement backed by the Obama administration that gives Congress some oversight.
Sen. Ted Cruz (R-Tex.), another presidential candidate, blamed Democratic resistance for the logjam.
"Right now, Democrats are blocking amendments because the Democrats don't want to vote on a requirement that Iran recognize Israel's right to exist as a Jewish state," said Cruz.
Senate Majority Leader Mitch McConnell (R-Ky.) will now have to decide whether to try to end debate on the Iran bill, thereby shielding it from controversial amendments, or to hold votes on those amendments. Another possibility is that everyone agrees on which amendments can come to a vote.
McConnell is still deciding what to do next, according to his top lieutenant.
"Right now we're a little balled up," said Sen. John Cornyn (R-Tex.). "But, I think there is some hope that we can get unstuck and start getting some votes on amendments and work forward to a conclusion."
Cornyn added: "It's going to take a little while for everybody to cool down and keep talking."