Paul had announced earlier on Tuesday that he intended to attach the amendment onto the Postal Service legislation, S. 1789.

Paul argued that it was relevant to the bill because the Postal Service is in danger of going bankrupt. Paul argued that discontinuing aid to Egypt could make money available that would help save the mail service.

"I would say it is relevant," Paul said. "I would say bring some of that money home and that would help fix the post office."

But Reid disagreed. He cut off Paul and then said he planned to fill all the amendments on the Postal Service bill himself, thereby blocking Paul or other Republicans from tacking on amendments.

Reid's decision seemed inevitable after Paul earlier on Tuesday said he planned to introduce legislation to stop sending aid to Egypt. After Paul made the announcement, Sen. Bernie SandersBernard (Bernie) SandersCynthia Nixon: 'Sometimes a little naiveté is exactly what is needed' George Clooney writes Parkland students: 'You make me proud of my country again' Lesson from special election: Run on Social Security, Medicare and lower drug prices MORE (I-Vt.) told reporters that the amendment seemed unrelated to the Postal Service legislation.

"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 said.

Paul and Reid's back and forth came after the Senate passed a cloture motion on whether to proceed on the Postal Service bill, called the 21st Century Postal Service Act.