That is easy to say, but not so easy to do.

“You have to be flexible,” said Andrew Williams, a Treasury Department spokesman. “You have to be clear that there is not a presumption of too big to fail. But you can’t give it up entirely because to do so may not allow you to avoid, in extremis, a major meltdown.” Lawrence H. Summers, the White House economic adviser, says there is no going back to the days of small banks. The financial world has moved on. “I don’t think you can completely turn back the clock,” he said.

Policy makers argue that shackling some of the very biggest banks with new rules will keep the behemoths from getting into trouble. The overhaul of financial regulation proposed last week by the Obama administration would provide so-called resolution powers that would allow big, complex financial institutions to, in fact, fail and let regulators take them over. The government could then wind down giant financial companies over time, as it does with smaller ones.

The administration also wants greater regulatory scrutiny and higher capital requirements for financial companies that pose so-called “systemic” threats. Details about these proposals are sparse, but the thinking is that investors would press companies to curb their risks and streamline their operations if bigness had some drawbacks.

That is not enough for some. Paul Volcker, the former Federal Reserve chairman and current White House adviser, for instance, has suggested that the government limit how much money big institutions can wager trading. The way things are now, banks reap profits if their trades pan out, but taxpayers can be stuck picking up the tab if their big bets sink the company.

Ms. Bair and others argue that the government should impose fees on giant banks to encourage them to operate more carefully and offset some of the costs of rescuing big institutions. The administration’s plan imposes such a charge only after a government rescue occurs.

Bigness has always been a powerful American theme. But in business, where many executives live by the creed of “Grow or Die,” it is dogma. Devotees of economic Darwinism insist that corporate size, and its accompanying economies of scale, brings progress and benefits to consumers.

But how big is too big to fail? And how would you measure it anyway? In the case of banks and giants like A.I.G. and Fannie Mae, policy makers argue that the interconnectedness of modern finance, as much as the size of the players, is the real issue. The collapse of one big financial company could cascade through the industry. In the case of General Motors and Chrysler, a failure could mean that thousands of jobs  not only at those companies, but at their suppliers as well  could evaporate.