McConnell made the request in the immediate aftermath of the Senate's shocking rejection of a scaled-back bill to repeal parts of ObamaCare, asking for unanimous consent to proceed to the defense legislation.

Senate Minority Leader Charles Schumer (D-N.Y.), who rejected Sen. John McCain's (R-Ariz.) request on Thursday to pause the healthcare debate and move on to the National Defense Authorization Act (NDAA), said after the healthcare vote that he would let the bill move forward.

But Paul, who has been among the Senate's most vocal ObamaCare critics, voiced an objection to McConnell's request without explaining why, stalling proceedings on the NDAA, which is typically one of the least controversial spending bills.

Instead, the Senate will take up judicial nominations when lawmakers meet on Monday.