Paul's announcement came just before the Senate voted 74 to 22 on a motion to move forward on cloture of the Postal Service bill.

It's not clear though whether Paul will even get a chance to add his amendment to the bill. Sen. Bernie SandersBernard (Bernie) SandersModerates see vindication in Lipinski’s primary win Sanders: Fox News 'couldn't handle' town hall on economic inequality Mississippi woman appointed to Senate, making Vermont only state to never have female lawmaker MORE (I-Vt.) urged Senate Majority Leader Harry ReidHarry Mason ReidTrump presses GOP to change Senate rules Only thing Defense’s UFO probe proves is power of political favors Nevada Democrat accused of sexual harassment reconsiders retirement: report MORE (D-Nev.) to only allow amendments related to the Postal Service.

"I would hope that every member of the Senate understands that this is a hugely important issue and that aid to Egypt doesn’t have a heck of a lot to do with saving the United States Postal Service," Sanders told reporters on Tuesday. "I would hope that we would have a debate on amendments dealing with the postal service. I think that is fair to the American people."

Paul's plan to introduce his amendment and Sanders's opposition to unrelated amendments to the Postal Service bill suggests that there could be another skirmish between Republicans and Democrats on amendments.

Republicans and Democrats previously came to a compromise over a highway transportation bill and unrelated amendments. After a series of negotiations, Reid allowed a limited number of amendments be tacked onto the highway bill in exchange for Republicans allowing a vote on a measure for the highway bill to move forward.