The pushback is reminiscent, in a way, of the executive branch's institutional opposition to oversight of the nation's intelligence agencies and operations. The Fed has always been shrouded in secrecy, and its leaders (in both the private and public sector) continue to insist on keeping their activities opaque, in order, they say, to protect complicated monetary policy from the political process.
It is believed that the Fed loaned major financial institutions upwards of $2 trillion during the financial crisis. Sanders' legislation would require the Government Accountability Office to conduct a comprehensive audit of the central bank, and force it to make public which companies received that money, and under what terms. Chairman Ben Bernanke opposes the latter on the grounds that exposing the institutions that required dramatic assistance would be counterproductive to the goal of restabilizing the financial system.
It's likely, in fact, that the Obama administration will be under intense pressure to veto the entire financial reform bill if "audit the fed" survives.
That's why, according to the Wall Street Journal they'll "fight to stop it at all costs." The White House is hoping to cut off "audit the Fed" in the Senate, so that they'll have a stronger hand when House and Senate negotiators meet to iron out the differences between their regulatory reform bills. If the Senate bill does not include Sanders' amendment, then the House will be in a weak position vis-a-vis the Senate and White House and the provision could be easily stripped.
If Sanders prevails, then the White House will be all but out of options and President Obama will likely be left with the choice of vetoing the legislation, or signing it and raising the ire of very powerful people. Stay tuned.