By Josh Rogin

Arkansas Sen. Tom Cotton said at a Bloomberg News breakfast Tuesday that he is pleased that Iranian negotiators are complaining about the letter he and 46 other Republican senators wrote them about their nuclear negotiations with the Obama administration.

Iranian officials reportedly raised the letter twice this week during negotiations with top U.S. officials. Secretary of State John Kerry and Iranian Foreign Minister Javad Zarif have been leading the talks, which restarted Sunday in Switzerland. The deadline for a political agreement between Iran and the P5+1 countries is Tuesday.

Cotton said that having the letter become part of the nuclear discussions was an indication of its success.

"They should be bringing up Congress' role.They should be asking the president if any deal could pass congressional muster, and if it doesn't, what does that mean," said Cotton. "That's one reason why we thought it was important to send the open letter to the leaders of Iran."

Cotton also responded to President Obama's harsh criticism of the letter. In an interview with Vice News, Obama said he was "embarrassed" for the Republican senators and that the missive was "close to unprecedented."

"The offer [to Iran] is indefensible, so they want to focus on process or ad hominem criticisms rather than try to defend the very bad deal they are on the verge of making," Cotton said. "Iran's leaders clearly have the message now."

Some Republican senators have backed off their enthusiasm for the letter. Cotton responded that the letter came after weeks of preparation, and that all 47 senators still support it. He also said he doubts that the blowback from the letter will harm GOP candidates in 2016.

"This is not [a treaty about] fishing rights with Canada; this is a nuclear agreement with the world's leading state sponsor of terrorism," he said. "The president seems to view Congress and the separation of powers as a nuisance."

The Senate's next action on Iran could come as early as next week, after the deadline for a political framework. Senate Foreign Relations Committee Chairman Bob Corker (R., Tenn.) intends to move forward on a bill he wrote with Sen. Bob Menendez (D., N.J.) that would mandate a 60-day congressional review of any Iran deal.

The White House has made it clear that the president would veto the Corker-Menendez bill, with White House chief of staff Denis McDonough saying it would "likely have a profoundly negative impact on the ongoing negotiations - emboldening Iranian hard-liners, inviting a counterproductive response from the Iranian [parliament]; differentiating the U.S. position from our allies in negotiations; and once again calling into question our ability to negotiate this deal."

If there is no political framework this month, Republicans will move forward with a new sanctions bill written by Menendez and Mark Kirk (R., Ill.). The White House has also publicly opposed that move. The administration's position is that Congress will get a vote only when the time comes to lift congressionally mandated sanctions.

Cotton, as a freshman senator, has been criticized as usurping the prerogative of the executive branch and upstaging his more senior colleagues. His response: "The question is not who has been in the Senate for 60 days versus who is in the Senate for 30 years. The question is who is right and who is wrong."

The fundamentals of the Iran debate remain the same. Obama's intention to make a deal will still anger lawmakers in both parties, and the drive to build a veto-proof majority for the Corker-Menendez bill is still picking up steam. The administration may have won the battle over the letter, but it could still lose its war to keep Congress on the sidelines.