Is the best way to end "too big to fail" cutting big banks down to size? Maybe. But it's unclear how taking a giant regulatory cleaver to the nation's largest banks would affect their customers.

In the wake of JPMorgan Chase & Co.'s multibillion-dollar loss on the international derivatives market known as the "London Whale" incident, the idea of breaking up the nation's megabanks has gained an influential endorsement from Sandy Weill, the former CEO of Citigroup who oversaw the merger of Citicorp and insurance giant Travelers Group in the 1990s, heralding the age of the "financial supermarket."

Powerful regulators, including Richard Fisher, president of the Dallas Federal Reserve Bank, and Thomas Hoenig, a member of the Federal Deposit Insurance Corp. board, also have expressed support for the idea.

The case for a breakup goes like this: As long as the deposits of Americans are sitting in the same institutions that have vast amounts of money invested in global markets, it's inevitable that the government will have to step in to bail them out should one of their bets go horribly wrong, as many did in the financial crisis, Weill told CNBC in July.

The solution? Break up the big banks, perhaps by reinstating the Glass-Steagall Act that once drew a dividing line between investment banks and consumer banks.

Lost in the debate is exactly how such a change would impact bank customers, particularly those who get investment management and insurance services from the same banks where they have their checking and savings accounts.

How to Break Up Banks

Determining the impact on consumers is difficult in part because "breaking up the banks" can mean a lot of different things, says Bert Ely, a banking consultant and principal of Ely & Co. Inc., in Alexandria, Va.

Simply reinstating the original Glass-Steagall Act would mostly affect the types of services banks could offer corporations and high-net-worth individuals, and would have little impact on day-to-day retail banking and investing, Ely says. But the original Glass-Steagall Act wasn't very effective at separating investment banks and commercial banks, he says.

"By the time it was repealed, Glass-Steagall had been eroded a lot," Ely says. "The bright line that supposedly had existed had gotten more blurry."

Steve Turner, a partner with financial services consulting firm Novantas, agrees.

"There was a separation between what (commercial) banks could do and what investment banks could do, but there was also a gray area around the kinds of brokerage activities that could be done," Turner says.

So far, the conversation has mostly focused on Glass-Steagall, which would have virtually no impact on consumer lending, investment management and other bank services for individuals, Turner says. But it's possible that legislators could go further to try and eliminate those gray areas.

"Are we talking about restricting what banks could do in terms of offering a broad array of financial services? Would you no longer be able to go to a bank and have a brokerage account where you can invest in stocks and bonds and mutual funds?" Turner says. "If that were restricted somehow by the way that the banks were separated, that could obviously have a big impact on the wealth management business of banks -- how they're advising some of their high-net-worth clients and providing them options."

It could also have an impact on retail investors and their individual retirement accounts with the bank and what investment options they might have, Turner says.

Indeed, a bill introduced in 2011, called the Return to Prudent Banking Act of 2011, goes further than the original Glass-Steagall Act. While the bill has little chance of passing, it would prohibit deposit-taking banks from being affiliated with any broker/dealer, investment adviser or investment company. In contrast, the Glass-Steagall Act allowed banks to trade in securities as long as it was on the orders of a customer.

If something like the Prudent Banking Act would pass, banks likely would have to spin off their investment management operations or sell them off to other companies. Either way, their customers who had formerly done all their financial activities in one place may no longer be able to do so and could be shuffled around in a subsequent wave of corporate reorganization.

Some benefits for Consumers

A more complete breakup of the big banks could have some upsides for consumers, says Dean Baker, economist and co-founder of the Center for Economic and Policy Research in Washington, D.C.

With market power spread around to more banks, consumers could see modest improvements in loan rates and savings yields as more and smaller institutions competed with each other.

"I think you would see some increased competition, some positive impact on prices," Baker says. "I don't think people would suddenly notice you can get a much better rate on savings or checking. I don't think there would be huge changes that way. There would be marginal ones that maybe we would be able to detect in the economic data."

Change Not Likely at the Moment

Whatever the impact on consumers, a government-driven breakup of the big banks is unlikely at the moment, Baker says.

"There's no powerful actor in either the Democratic or the Republican Party that's really pushing it at this point," he says.

Ely agrees. "Big banks aren't going to get broken up. There's no legal foundation now, and I doubt Congress will act to create one," Ely says. "What I think we'll see instead is more market-driven restructuring -- banks voluntarily pulling out of certain markets."

Still, there is one thing that could move a bank breakup plan beyond cable news shows and onto a congressional docket, Baker says.

"The set of events that might get you to a Glass-Steagall or a breakup of the banks would be another catastrophic event. It would be like the London Whale, but one that actually brought down a major bank and forced a bailout," he says. "That could happen, but I don't think it's very likely."