Federal Reserve Board Governor Daniel Tarullo’s call for limiting bank size is sparking debate in unexpected places. Keith Hennessey, who ran the National Economic Council under President Bush, was in Chicago late last week for a discussion with Democratic lawmaker Barney Frank. The topic of the panel, sponsored by CME Group Inc., was the housing crisis.

But the most spirited exchange took place after Hennessey said that banks are simply too big to regulate adequately. “I think Tarullo has got a good point,” he said, referring to Tarullo’s argument for the need to cap bank size. Hennessey, as Bush’s economic policy assistant in 2008, was among administration officials that worked to win Congressional approval for the bailout of insurance major AIG, as its failure threatened to plunge the nation’s financial markets, already reeling from the failure of Lehman Brothers, even deeper into crisis.

Lawmakers eventually relented. On Friday, Frank, who co-authored Wall Street reform legislation designed to prevent another bailout of a too-big-to-fail financial institutions, was not about to cede ground this time to Hennessey. “I didn’t ask what Tarullo thinks – are you for breaking up the banks, and if so, to what size, and by what method?”  “Right now I don’t see any better solution than what Tarullo has suggested – yes, a size cap on banks… The alternative is a repeat of the 2008 crisis.” After the panel, Frank said he took issue with the idea, both from a technical perspective – “How do you do it? Do you sell it? Who’s going to buy it? The other banks by definition can’t.” – and because of concern that trimming bank size will hurt the ability of U.S. financial institutions to compete internationally.