The Federal Reserve is once again in lawmakers’ cross-hairs, with the latest salvo coming from the influential head of the Senate Banking Committee.

Alabama Republican Richard Shelby unveiled a proposal Tuesday that would not only increase congressional oversight of the nation’s central bank, but also shift the balance of power within the Fed. Among other things, the bill would allow the Fed’s regional presidents -- not just the Washington-based board of governors -- to set the interest rate on excess reserves that banks park at the Fed, a new tool that officials believe will be instrumental when they begin to raise interest rates. It would also require the head of the New York Fed to be nominated by the president and confirmed by the Senate. Currently, that person is appointed by the bank’s board of directors.

Those proposals are just one piece of the much larger bill titled the “Financial Regulatory Improvement Act." And in fact, the Fed is not the focus of the proposed legislation, which is ostensibly intended to protect community banks and credit unions from some of the regulatory burdens of the sweeping financial reform bill passed five years ago.

The 10 Democrats on the committee have voiced unanimous opposition to the far-reaching scope of the bill. Committee staffers pointed out that President Obama has already threatened to veto two provisions included in Shelby’s proposal: one that would change the definition of mortgages that receive certain legal protections and another that could allow more expensive loans for those buying mobile homes. That led Democrats to “question the seriousness of the proposal,” according to one staffer.

Still, the bill marks a shift in lawmakers’ strategy to rein in the Fed’s powers -- an effort that has been underway since the central bank’s bold but controversial moves to stem the financial crisis and resuscitate the economy. Calls to audit the Fed or mandate how it conducts monetary policy have struggled to gain broad support. But lawmakers of both parties seem open to democratizing the Fed’s power structure. The idea in Shelby’s bill that the head of the New York Fed should be subject to public confirmation was originally proposed by Democratic Sen. Jack Reed of Rhode Island.

“Federal Reserve reform is an issue where the far-right and the far-left on Capitol Hill find themselves in agreement,” said Isaac Boltansky, senior vice president at Compass Point Research. “Whether as part of this legislative package or as a stand-alone bill, [the issue] is likely to win support from both sides of the aisle.”

Though aides said Democratic lawmakers opposed including the Fed in this legislation, the provisions on their own could merit further discussion.

Central bank officials seem to recognize that threat. Fed Chair Janet Yellen met with Shelby in March for nearly half an hour, though neither has said whether they discussed restructuring the Fed. But San Francisco Fed President John Williams addressed the issue of central bank independence in a essay released Monday.

"The independence dilemma stems from the enormous power central banks have to create money essentially out of thin air," he said. "Successful monetary policy necessitates both an arm's-length relationship to the political process and oversight by elected officials."