Senator Rand Paul (R., Ky.) introduced a bill (S.264), which is popularly known as "Audit the Fed" (ATF). The bill picked up 30 initial co-sponsors. Although the Fed is already extensively audited in the accounting sense of the term, the ATF bill would expand the scope and scale of Fed auditing. Indeed, monetary policy decisions, which have been exempt from any sort of "auditing" since 1978, would see their auditing exemption lifted if the bill becomes law.
There is popular support for the idea that the Fed should be audited. More than three-quarters of registered voters would give the general idea of auditing the Fed a green light. It's no surprise, then, that there has been bipartisan support for similar proposals in the past. However, none of these have become law because the push-back from Fed officials and other "experts" has been strong. Today is no different, with the Fed and the Obama White House all singing the same tune: "It's Dangerous."
The real issue at stake is whether the Fed should be independent. The opponents of the ATF bill naturally think that the law would imperil the Fed's autonomy and that this would be objectionable.
What would Milton Friedman say? Well, we don't know for certain because he is unfortunately unable to read S.264. That said, Friedman weighed in on the issue of central bank independence on several occasions. Indeed, an essay he penned in 1962 was titled "Should there be an Independent Monetary Authority?" (In: In Search of a Monetary Constitution, edited by Leland B. Yeager, Harvard University Press). Friedman concluded that "The case against a fully independent central bank is strong indeed." Milton Friedman's position on this issue was quite clear at the time. There is little doubt as to whether he would see the situation at hand any differently.