The Texan wants to name the street "Oswaldo Payá Way" after a Cuban dissident.
Reid's remarks come after Sen. Patty Murray (D-Wash.) pulled her bill from being voted on.
But the administration says it doesn't have the agreements between Iran and the IAEA.
But the legislation still faces challenges from both sides.
The letter comes after Susan Rice acknowledged the so-called “side” agreements.
Sen. Joe Manchin is the only Democrat on the letter.
The move comes as Republican senators seek an investigation into Planned Parenthood.
Senate Republicans lined up the floor Wednesday to voice their concerns.
The Republican leader said senators will try again on Wednesday.
"We know the cost of war. We know it in human lives," he said.