Organized by freshman Senator Tom Cotton and signed by the chamber's entire party leadership as well as potential 2016 presidential contenders Marco Rubio, Ted Cruz and Rand Paul, the letter is meant not just to discourage the Iranian regime from signing a deal but also to pressure the White House into giving Congress some authority over the process.

"It has come to our attention while observing your nuclear negotiations with our government that you may not fully understand our constitutional system … Anything not approved by Congress is a mere executive agreement," the senators wrote. "The next president could revoke such an executive agreement with the stroke of a pen and future Congresses could modify the terms of the agreement at any time."