The independent counsel law was thrown out by SCOTUS after Billy Jeff's impeachment. They decided it was a violation of the separation of powers - only the executive branch has the ability to prosecute anyone. The only powers that Congress has are the power of the purse and impeachment - for anything else, such as lawbreaking by the executive branch, they must rely on the executive branch to prosecute itself...
Boehner can go to a Federal Court and seek a recusal of the Attorney General and make an application for a Independent Counsel to the Inspector General. That is what the next move should be.