Sen. Rand Paul is getting a lot of attention this morning for his threat to hold up the nomination of Janet L. Yellen to head the Federal Reserve, but he may have very little leverage to stop her confirmation.

The Kentucky Republican is seeking a vote on his Federal Reserve transparency legislation as part of considering the Yellen nomination. The announcement came in a YouTube video posted Thursday by the Campaign for Liberty, a nonprofit affiliated with Paul’s father, former Rep. Ron Paul, R-Texas.

Legislation to require an audit of the Federal Reserve has had bipartisan support in the past when pushed by both Pauls, but it has faced no shortage of opposition and roadblocks.

“Sen. Rand Paul will be demanding a vote on audit the Fed in the Senate when they consider the new Fed nominee,” John Tate, the chairman of Campaign for Liberty, said in the video.

However, Majority Leader Harry Reid, D-Nev., could decide to ignore Paul’s request by moving to limit debate on Yellen’s nomination by filing cloture. If Reid gets 60 votes, there’s no need to make a deal with Paul or anyone else. Yellen appears to already have enough support to overcome a filibuster, unless Republicans and some sympathetic Democrats decide to back his quest for a vote on the audit bill.

“Right now, the Senate is preparing to debate and confirm the new Obama nominee to chair the Federal Reserve,” Paul said. “I say vote no on a new Fed chairman without a vote on my audit the Fed bill. This will be the fight of our lives.”

In the video, Tate makes a claim that won’t be true unless Paul can line up at least 41 votes to sustain a filibuster of Yellen.

“This is an historic opportunity in the Senate,” Tate said. “Majority Leader Harry Reid has blocked this vote for over two years, but he is out of options now if he wants a vote on his Fed nominee.”

When CNBC reported Paul intended to place a hold on the Yellen nomination Friday morning, the stock market seemed to react, even though the Campaign for Liberty effort was online Thursday.