Hoyer: Republicans have the 'right' to pressure Fed

The other side of that coin, Hoyer noted, is that the independent Fed is under no obligation to listen to lawmakers. While the central bank's mandate is set by Congress, it does not have to seek legislative approval for policy moves.

"They have the right to do it, and of course the Fed, as an independent body, has the right to say, 'Well, thank you very much, but we don't agree,'" Hoyer said.

Top Republicans in the House and Senate sent the letter to Fed Chairman Ben Bernanke on Monday, detailing "serious concerns" they had about further intervention, because they say previous efforts have done more harm than good.

"The American people have reason to be skeptical of the Federal Reserve vastly increasing its role in the economy if measurable outcomes cannot be demonstrated," the lawmakers wrote.

The letter came one day before a highly anticipated meeting of the Fed's Federal Open Market Committee, which sets Fed policy. With the economic recovery slowing down, many have anticipated the Fed will take further steps in an attempt to boost economic growth.

But Republicans have vocally criticized previous such efforts, arguing that they had little effect and devalued the dollar.