It's one that could turn ugly in November if the GOP manages to score big.
Where Paul has been the lone voice in the wilderness criticizing the central bank for years, others in the GOP recently adopted the Fed as a scapegoat for the financial crisis of 2008.
Many of the Republican attacks include calls to fire Fed Chairman Ben S. Bernanke and to scale back the Fed's mandate - or in Paul's case, eradicate it altogether.
And while Paul - who actually wrote a book called "End the Fed" in 2008 - has little chance of becoming the nominee, his campaign does have a larger philosophical objective.
"It is Paul's goal to permanently establish within the Republican Party a group that is dead set on not having the Fed," Douglas Holtz-Eakin, chief economic adviser to Sen. John McCain, R-AZ, during his 2008 run for the presidency,told MarketWatch. "This is not going away."
Ron Paul Scores Big With Younger VotersAlthough Paul's overall support generally hovers in the low double digits, his message is very popular among younger Republican voters.
Paul won 48% of the under-30 vote in Iowa, 47% of the under-30 vote in New Hampshire and 31% in South Carolina. It's a demographic every candidate covets.
Paul's resonance with young voters, combined with the public's dim view of the Fed has set off an all-out GOP assault on the central bank.
For added juice, Republicans in general have sought to tie their criticisms of the Fed to U.S. President Barack Obama and the Democrats.
"If you are a [Republican] running for Congress - those freshmen in the House - they thought that Bernanke was walking around talking about buying assets for Obama to make it easier for him to spend," Holtz-Eakin told MarketWatch. "It lit the fuse."
Following Ron Paul's LeadGingrich, whose presidential campaign has been on an upswing of late, has come the closest to Paul's radical positions. The former Speaker of the House has said he would eliminate the unemployment mandate of the Federal Reserve, forcing it to focus on inflation alone.
Gingrich also has vowed to seek Bernanke's resignation if elected president.
Meanwhile, former Massachusetts governor Mitt Romney has now moved from qualified support for Bernanke and the Fed early in the campaign to a more negative position. He would seek Bernanke's removal, as well.
"I'd be looking for somebody new," Romney said in one of the many debates. "I think Bernanke has over-inflated the amount of currency he's created. QE2 did not work."
Only Rick Santorum, the former Pennsylvania senator, has avoided discussing the Fed, although he has said that it should have its mandate reduced to include only inflation.
Most of the Republican candidates who have dropped out also took shots at the Fed, with Texas Governor Rick Perry going so far as to label Bernanke "treasonous" for his easy money policies.
With such vitriol increasingly becoming part of mainstream GOP thinking, a Republican in the White House - and possibly control of both houses of Congress - could set the stage for more than just fiery anti-Fed talk.
Can They Really End the Fed?Regardless how eager Republicans are to make changes at the Federal Reserve, they're sure to find it's not as easy to pull off as they'd like their campaign audiences to believe.
Just last fall, GOP congressional leaders sent a letter to the Federal Open Market Committee (FOMC) to dissuade them from following through on a plan, known as "Operation Twist," to sell short-term Treasuries while buying longer-term Treasuries.
The FOMC ignored the letter and voted to approve the measure.
In fact, Congress created the Federal Reserve in 1913 to be an apolitical, independent central bank. The seven members of the Board of Governors, which comprise the majority of the policy-making FOMC, are appointed by the president and confirmed by the Senate, but getting rid of them is not so easy.
Fed governors (including the chairman) serve 14-year terms that expire in January of even-numbered years. According to law they "may not be removed from office for their policy views," which could complicate GOP plans to remove Bernanke.
President Richard Nixon discovered just that in late 1968 when he sought to replace Chairman William McChesney Martin Jr. with Arthur Burns. President Nixon offered Martin the position of Secretary of the Treasury to open up the Fed chairmanship to Burns.
But Martin, seeing through the ruse, turned down the offer and served out his term. President Nixon was forced to wait until Martin's term expired in 1970 to appoint Burns to the post.
Chinks in the Fed's ArmorOf course, that doesn't mean Republicans are entirely without options. They could conceivably pass legislation changing the Fed's mandate if they control both Congress and the White House.
Although it's unclear how the markets would react, Wall Street would probably balk at such a fundamental change to the body that sets the nation's monetary policy.
However, Paul proved two years ago that the Fed is not invulnerable when he successfully added a provision to the Dodd-Frank law that allowed for an audit of the central bank.
And as long as Paul's "end the Fed" message is gaining traction among rank-and-file Republicans - especially the younger set -attacks on the Fed are unlikely to stop.
"In the minds of the public, the Fed was the great enabler of this huge catastrophe that we've had since the panic of 2008," Steve Hanke, a professor at Johns Hopkins University and senior fellow at the Cato Institute, told Slate magazine. "And I think the general consensus is that they remain the source of a lot of the problems we're facing right now as well."
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The Federal Reserve:
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The Fiscal Times:
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