Sen. Bernie Sanders, I-Vt., introduced legislation on Wednesday to break up the nation's six biggest banks — JPMorgan Chase, Bank of America, Citigroup, Wells Fargo, Goldman Sachs and Morgan Stanley.

Sanders' Too Big to Fail, Too Big to Exist bill would cap the size of the largest financial institutions so that a company's total exposure is no more than 3% of GDP, about $584 billion today, the bill states. The bill would also address large nonbank financial service companies such as Prudential, MetLife and AIG.

Rep. Brad Sherman, D-Calif., plans to introduce a companion bill in the House.

"No financial institution should be so large that its failure would cause catastrophic risk to millions of Americans or to our nation's economic well-being," Sanders said in a statement. "We must end, once and for all, the scheme that is nothing more than a free insurance policy for Wall Street: the policy of 'too big to fail.'"

As it stands now, the six largest banks in America "control assets equivalent to more than half the country's GDP and the four largest banks are on average about 80% larger today than they were before the bailout," Sanders said, noting the 10-year anniversary of the Wall Street bailout.

These "Too Big to Exist" institutions would no longer be eligible for a taxpayer bailout from the Federal Reserve and could not use customers' bank deposits to speculate on derivatives or other risky financial activities, Sherman added.

Sherman stated in the statement that JPMorgan Chase and Bank of America "would be forced to shrink to where the banks were in 1998."

Wells Fargo, he said, "would go down in size to where it was in 2005. And Citigroup would shrink to where it was during the second term of [former President] Bill Clinton's administration."

Better Markets, a group that supports financial regulation, stated Thursday that "whether people agree or disagree with the details [of Sanders' bill], we hope that Sen. Sanders' bill to break up the biggest too-big-to-fail banks will reignite an important discussion about how to remove that threat to the country and about how to get banks back into actual banking again."

The problem, Better Markets continued, "isn't just that these gigantic banks are too-big-to-fail.  It's that they also remain too-big-to-manage and too-big-to-jail, as the weekly headlines of their latest wrongdoing and criminality remind everyone."

Dennis Kelleher, president and CEO of Better Markets, told ThinkAdvisor in an email message that Sanders "and others are seeking to address the lethal problems posed by too-big-to-fail, too-big-to-jail, too-big-to-manage and too-big-to-regulate financial institutions."

Given the banks' "ongoing system risks, threat to taxpayers, egregious predatory conduct, and socially useless bonus-focused business models, it's only a matter a time before Sen. Sanders' bill or something like it passes."

The Too Big to Fail, Too Big to Exist legislation "is short and to the point," says Simon Johnson, former chief economist at the International Monetary Fund and current professor at the Massachusetts Institute of Technology, in a statement released by Sanders.

"The largest banks and other highly leveraged financial institutions are simply too big — and pose a real danger to our continued economic recovery. Make them break up into smaller pieces, bringing more competition, better service and lower risks for the American economy," Johnson said.