Treasury Secretary Timothy Geithner testified in the House today on his plan for addressing too-big-to-fail financial institutions. And it didn’t take long for lawmakers to attack the proposal, from how it would fund the resolution of failing firms (first by taxpayers, then recouped through fees on other institutions) to the decision to put broad powers in the Federal Reserve.

The draft legislation released by House Financial Services Committee Chairman Barney Frank establishes a council of regulators to monitor risks across the financial system. But the Fed would get the most power in what’s described as “backup” authority to take action when the council does not.

“Although it’s not singled out as a systemic uber-regulator in name, don’t anyone be fooled,” said Republican Rep. Scott Garrett of New Jersey. “The Fed is given primary supervision over systemic firms and can override lesser regulators that don’t comply with its wishes. In the name of mitigating systemic risk, the Fed is given almost unlimited authority to systemically dismantle a private company. … I’m very uncomfortable with the sweeping, unchecked power of the same entity that failed to effectively mitigate many of the large bank holding companies already under its purview.”

Mr. Geithner said Congress and the administration must “close loopholes and reduce possibilities for gaming the system.” The proposed Financial Services Oversight Council would identify firms that pose a systemic threat and put them under heightened supervision. But the Fed, he said, “would oversee individual major financial firms so that there is clear, inescapable, single-point accountability.”

In prepared testimony, Fed governor Daniel Tarullo effectively endorsed the legislation. He said the Fed’s Board of Governors believes the proposal “provides a strong framework for achieving a safer, more stable financial system.” But Sheila Bair, chairman of the Federal Deposit Insurance Corp., said the oversight council as outlined in the proposal “currently lacks sufficient authority to effectively address systemic risks.”