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 SandersBernie SandersSanders: Trump budget ‘must be defeated’ The Hill's 12:30 Report Sanders will 'absolutely' work with Trump to lower prescription drug costs MORE (I-Vt.) urged Senate Majority Leader Harry ReidHarry ReidAfter healthcare fail, 4 ways to revise conservative playbook Dem senator 'not inclined to filibuster' Gorsuch This obscure Senate rule could let VP Mike Pence fully repeal ObamaCare once and for all 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.