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) SandersWorld leaders reach agreement on trade deal without United States: report Sanders on Brazile revelations: DNC needs ‘far more transparency’ Sen. Warren sold out the DNC MORE (I-Vt.) urged Senate Majority Leader Harry ReidHarry ReidTop Lobbyists 2017: Grass roots Boehner confronted Reid after criticism from Senate floor GOP in uncharted territory rolling back rules through resolutions 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.