WASHINGTON — Federal Reserve Board Chair Janet Yellen is facing the first real test to her agency's independence during her tenure, as House Republicans push a bill designed to broaden congressional oversight of the central bank and tie its hands regarding monetary policy.

Since the Fed's creation a century ago, it has had to fight to preserve itself from what it sees as congressional meddling and political influence.

But Yellen faces a far more significant and specific threat under the GOP plan, which could gain additional momentum if the Republicans seize the Senate after the November elections.

"This is a long-standing challenge for the Fed," said Karen Shaw Petrou, a managing partner at Federal Financial Analytics Inc. "There's always been a deep-seated populist distrust of the central bank. It's the reason it took the country decades to establish one, despite financial crises. I think it's fascinating at the Fed's centenary just how alive that same sentiment is a hundred years later."

To be sure, political pressures on the central bank have waxed and waned over the years, depending on the health of the U.S. economy and the mood of the country. For Yellen, the current danger comes amid a backdrop of uncertainty and a weak economy as she leads the Fed out of its unprecedented economic stimulus program, known as quantitative easing, and begins charting a course to unwind the bank's balance sheet, and eventually lifting rates.

"Until the Fed seriously begins to unwind the balance sheet and test how quickly they can exit current policy, the current pressure is not going to change at all until we get to that point," said Brian Gardner, a policy analyst at Keefe, Bruyette & Woods. "And then it's either going to subside because the Fed handles it well or it will intensify because there are some glitches in the system and it doesn't go as well as they wanted to."

To many on Capitol Hill and elsewhere, Yellen's era is viewed as a continuation of former Fed Chairman Ben Bernanke's policies. But scrutiny of those polices has only increased since Yellen took the helm, some said.

"I think that issue is on steroids today because of QE and this notion that the Fed is this extragovernmental organization that's run amuck," said Cornelius Hurley, director of the Boston University Center for Finance, Law & Policy. "That has a certain amount of cachet both in the economics community, but particularly in the Tea Party and GOP wing."

The Republican bill, called the Federal Reserve Accountability and Transparency Act, is sponsored by Reps. Bill Huizenga of Michigan and Scott Garrett of New Jersey. It would require the central bank's policy setting body to describe a strategy for how it would adjust interest rates. The Federal Open Market Committee could later alter the rule, but any changes would have to be reviewed by the Government Accountability Office.

The bill would also require more transparency over the Fed's bank oversight and require the central bank's chair to appear before Congress quarterly, instead of twice a year as stipulated in the current law. (Huizenga is vice chairman of the Financial Services subcommittee on monetary policy and Garrett is chairman of capital markets and government-sponsored enterprises.)

Observers, however, argue the aim of the GOP plan is not transparency, but rather control over the central bank.

"The Fed is and ever will be a controversial institution," said an industry source, who declined to be named given the sensitivity of the issue. "But there are a lot of reasons I would argue that the FRAT Act goes away over the line. It's not after accountability, it's after control."

Alan Blinder, a professor of economics at Princeton University and former vice chair of the Fed, has called the legislation a "dreadful bill."

While he said the legislation took steps to increase accountability and transparency such as trimming news blackout periods, it also introduced dubious measures like publicly disclosing in advance before entering international negotiations.

"The meat and potatoes of the House bill has little to do with either transparency or accountability," Blinder wrote in an op-ed piece in The Wall Street Journal. "Instead, it seeks to intrude on the Fed's ability to conduct an independent monetary policy, free of political interference."

While the Financial Services Committee approved the bill by a split vote of 32 to 26 last week, the chances it will become law remain slim. But it could gain more traction if the Democrats lose the Senate. Sen. Richard Shelby, who is expected to become chairman of the Banking Committee if the GOP win the Senate, is a longtime critic of the Fed who voted against Yellen's nomination on ideological grounds.

"On the one hand, it's harmless, but on the other hand, it's not, because we have an election coming up in November and there's a 60% chance the Senate is going to become Republican-controlled," said Hurley. "So the ideas that seem wacko in the House could get a hearing in the Senate. The last line of defense would be the president's veto."

Yellen has already voiced her opposition to the bill, saying it's an error "tying monetary policy to a rigid mathematical formula to any rule."

"It would be a grave mistake for the Fed to commit to conduct monetary policy according to a mathematical rule," Yellen said while testifying on Capitol Hill last month. "No central bank does that."

Although the bill would allow the Fed to depart from the rule if it was warranted, the measure would still inevitably compromise the Fed's independence, Yellen said. It would also be "strait jacketing" how the FOMC set monetary policy rather than informing Congress and the public of the rationale of its decision making, she said.

"Political scrutiny would essentially undermine central bank independence in the conduct of monetary policy, and I believe that global experience has shown that we have better macroeconomic performance when central banks are removed from short-term political pressure," she said.

This is not the first time a Fed chair has had to push back against legislative efforts to provide direct congressional oversight of the U.S. central bank's policymaking.

Bernanke repeatedly fought back efforts by former Republican Rep. Ron Paul to audit the central bank's monetary policy decision in order to have greater oversight on the Fed's decisions, particularly how interest rates were set.

"It should be up to the Fed to make monetary policy decisions independently of short-term political influences with an eye for long-term objectives of the economy," said Bernanke, in a November 2011 speech.

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