The chart above is from a recent Rasmussen Poll (done on November 6th and 7th of 1,000 nationwide adults, with a 3 point margin of error). It shows that about 3 out of 4 Americans (74%) agree that the Federal Reserve should be audited. I normally don't care for the proposals put forth by congressional Republicans, but I agree with this one -- not because I want to embarrass the president, but because I think all federal departments and programs should be audited on a regular basis (regardless of which party holds the White House).
Regular audits can accomplish two goals. First, if there is a problem discovered then it will be exposed and can be fixed (before it gets even worse). And second, those audits can assure the general public that government officials are doing their jobs in an appropriate and competent manner. There should be no secrets in any government department or program in a democracy, because the people have a need to know what is going on (so they can vote with knowledge). Government transparency is essential in any democracy.