The U.S. government would be given broad new powers to shrink financial firms deemed "too big to fail" and shift the cost of rescuing troubled companies from taxpayers to other large firms, according to draft legislation released Tuesday.

Testifying before lawmakers Thursday, Ben Bernanke reiterated a call for the Fed to be given supervisory powers over institutions that pose a systemic risk to the financial system, and proposed that a council of regulators help monitor risk.