Four of the 47 Republican senators who signed a letter to Iran’s Islamic regime about the constitutional role of Congress are prospective candidates for president, and they stuck to their guns in the face of harsh criticism of the letter from Democrats and media pundits.

One, Sen. Rand Paul, R-Ky., said today on Glenn Beck’s radio show the notion that he regrets signing the letter is “kind of crazy.”

“Do I have any regrets about informing another country of how our Constitution works?” Paul said.

The other presidential hopefuls joining Paul were Ted Cruz of Texas, Lindsey Graham of South Carolina and Marco Rubio of Florida.

Sen. Tom Cotton, R-Ark., authored the open letter sent Monday to the leaders of Iran regarding their ongoing nuclear negotiations with the Obama administration.

“It has come to our attention while observing your nuclear negotiations with our government that you may not fully understand our constitutional system,” Cotton wrote.

“The moment he told Congress basically to go to hell, I wanted him and the Iranians and the world to know you can’t deal us out,” says @GrahamBlog

The president negotiates international agreements, Cotton wrote, and Congress must approve them. Without such approval, any deal reached is merely “an executive agreement between President Obama and Ayatollah Khamenei.”

Forty-six of Cotton’s Republican colleagues in the Senate signed the letter.

During a press conference Tuesday where she addressed the controversy surrounding her private email server, former Secretary of State Hillary Clinton, the Democratic favorite for president, said the Republican senators’ letter was “out of step with the best traditions of American leadership.”

In a statement, Vice President Joe Biden said the letter was “expressly designed to undercut a sitting president in the midst of sensitive international negotiations” and “beneath the dignity” of the Senate.

In a front-page headline, the New York Daily News labeled the signatories “traitors.”

Rubio told NBC News on Tuesday that he “would send another one tomorrow.”

“I think the risk of a nuclear Iran is so great that we need to do everything possible to keep us from finding us in a situation where we are going to have a nuclear Iran,” Rubio said.

Cruz told CNN on Tuesday he wishes the Obama administration “showed even a fraction of the seriousness and backbone toward Iran that they should manifest in terms of hostility to Congress.”

“The Constitution requires that any treaty be submitted to the Senate for ratification,” Cruz said, adding:

Unfortunately, President Obama has repeatedly defied the law and defied the Constitution. And this Iran deal I believe is a historic mistake. I believe it endangers the national security of this country.

Graham told Bill Hemmer on Fox News’ “America’s Newsroom” today that he signed the letter because the president threatened to veto “bipartisan legislation” on Iran:

The moment he told Congress basically to go to hell, I wanted him and the Iranians and the world to know you can’t deal us out. So, if he’s contemplating a deal to give congressional sanction relief and not allow us to have a say, he’s flat wrong and that’s why I signed the letter.

The four senators aren’t the only GOP presidential hopefuls who have signed the letter. Cotton’s office confirmed in a statement that Louisiana Gov. Bobby Jindal has added his name.

Jindal tweeted that all presidential hopefuls should sign the letter.

Jindal also criticized Biden and Clinton for their comments about the letter.

Seven Republican senators did not sign the letter.

Sen. Bob Corker, R-Tenn., chairman of the Foreign Relations Committee, told Roll Call he declined because he hopes bipartisan legislation still can be passed.

“The role I’m trying to play is to get to … an outcome, and you know it wasn’t appropriate for me to sign onto the letter,” Corker said.

His fellow senator from Tennessee, Lamar Alexander, also declined to sign the letter. The other GOP senators who didn’t are Thad Cochran of Mississippi, Lisa Murkowski of Alaska, Daniel Coats of Indiana, Susan Collins of Maine and Jeff Flake of Arizona.