On Tuesday, House Speaker John Boehner, R-Ohio, refused to join his fellow Republicans in criticizing President Obama over the " hot mic " comments the president made to the president of Russia at a summit in South Korea.

"When the president is overseas," Boehner told reporters, "I think it's appropriate that people not be critical of him or our country."

But now it's Wednesday and the president is back in the U.S., and Boehner clearly feels no such restraints, having sent a letter to the president saying he was "alarmed to learn of the message you sent to incoming Russian President Vladimir Putin while in South Korea Monday."

ABC News obtained a copy of the letter after the White House received it Wednesday afternoon.

To recap, on Monday at the Nuclear Security Summit in Seoul, South Korea, President Obama whispered to Russian President Dmitri Medvedev that he would have "more flexibility" to deal with controversial issues such as missile defense after the 2012 elections, and that incoming Russian President Vladimir Putin needs to give him "space." The exchange was picked up by microphones as reporters were let into the room for remarks by the two leaders.

When asked to explain what President Obama meant, deputy national security adviser for strategic communications Ben Rhodes told ABC News that there is room for the U.S. and Russia to reach an accommodation, but "there is a lot of rhetoric around this issue - there always is - in both countries."

GOP presidential front-runner Mitt Romney pounced on the remarks - ignoring the "water's edge" tradition that Boehner respected - saying that Russia is "without question our number one geopolitical foe. They fight every cause for the world's worst actors. The idea that he has more flexibility in mind for Russia is very, very troubling indeed."

Boehner in a letter to the president today, expressed similar concerns, writing:

"America's missile defense program is critical to our homeland security and the collective security of our NATO partners, and it has clear implications for the security of our allies in the Middle East.  I and other Members of the House have previously expressed concern about your administration's apparent willingness to make unilateral concessions to Russia that undermine our missile defense capabilities.  Your comments reinforce those worries.

"The Russian government has not lived up to its obligations to support the world community in reining in the rogue nations of Iran, Syria, and North Korea.  On the contrary, Russia has at times offered support for these dangerous regimes.  And it is increasingly evident that Russia is intent on expanding its boundaries and power through hostile acts - including invading a neighboring American ally.  It is troubling that you would suggest to Russian leaders that their reckless ambition would be rewarded with greater 'flexibility' on our missile defense program after the upcoming election.  That has significant implications for the security of our homeland, sends a terrible signal to our allies around the world, and calls into question the effectiveness of your 'reset' policy with the Russian government.

"Your message also implies you understand such concessions would not be supported by the American people or the Congress.  As you know, the House has passed legislation prohibiting the administration from making any agreements to diminish our missile defense capacity absent congressional authorization or treaty.  This is an imperative upon which we continue to insist."

President Obama attempted to clarify his remarks at the summit, saying that "arms control is extraordinarily complex, very technical, and the only way it gets done is if you can consult and build a strong understanding, both between countries and within countries," he said. "I don't think it's any surprise that you can't start that a few months before presidential and congressional elections in the United States, and at a time when they just completed elections in Russia…The only way I get this stuff done is if I'm consulting with the Pentagon, with Congress, if I've got bipartisan support and frankly, the current environment is not conducive to those kinds of thoughtful consultations."

The president insisted that "I think everybody understands that - if they haven't they haven't been listening to my speeches - I want to reduce our nuclear stockpiles.  And one of the barriers to doing that is building trust and cooperation around missile defense issues.  And so this is not a matter of hiding the ball, I'm on record. … I want to see us, over time, gradually, systematically, reduce reliance on nuclear weapons."

Boehner wrote that he found this explanation unsatisfying.

"Your immediate clarification provided little clarity and instead sought to conflate the issue of missile defense - the focus of your words - with the separate matter of Russia's nuclear weapons program," Boehner said. "I ask that you explain what greater 'flexibility' on missile defense you were suggesting Mr. Putin could expect in a second term.  With Congress' expressed interest in this matter and America's objective of preventing rogue states from launching missile strikes, it is important to know what changes you are contemplating or offering. Further, what actions does your administration believe the Russians have taken that warrant any change in our missile defense policy?"

He concluded: "Given the specter you have raised of shifting positions, it would be appropriate that you state publicly and clearly that no unilateral concessions will be made to the Russians, before or after the election.  Or, if your administration is planning any concessions to the Russians on missile defense, I request that you report on them and consult immediately with the congressional committees of jurisdiction.  A misguided missile defense policy would have far-reaching consequences, and any concessions you may have under consideration require an open and thorough justification.  A post-election surprise on this critical issue would not be welcomed by the American people, the Congress, or the world community."

Boehner isn't the only Republican to make an issue of this now that the president is back in the U.S. On CNN last night, former Bush White House press secretary Ari Fleischer asked Obama's deputy campaign manager Stephanie Cutter, "can she assure us that the president has made no other statements like that to, say, Arab leaders or Palestinian leaders, 'Give me space and after the election I'll have more flexibility to deal with Israel?' Can you assure us he's not done that?"

Cutter said that the "president has the strongest foreign policy record of a sitting president in generations. And those are the facts that remain true. And if there's one thing that voters don't doubt in this election is the ability of this president to keep this country safe and make the right foreign policy decisions based on sound judgment.  He's not going back and forth unlike some potential opponents of ours."

-Jake Tapper