The Democrats will never let Rand control the Senate floor to do that again.
What Rand was thinking about doing was force the Senate to get 60 votes to overcome a filibuster. He got attacked by other Senators today for wanting Congress to debate and vote on AUMF but would then filibuster to prevent a debate.
He got what he wanted in terms of Congress actually voting on a AUMF. The fight now moves to the House where there's a chance to defeat it.