In the six years since Congress passed aggressive Wall Street overhauls, regulators have implemented thousands of pages of new rules aimed at preventing another taxpayer bailout of “too big to fail” banks.

But, so far, the task is proving a tough challenge.

Five of the country’s largest banks, including JPMorgan Chase and Bank of America, still do not have credible plans for winding down their operations without taxpayer help if they start to fail, the Federal Reserve and the Federal Deposit Insurance Corp. said Wednesday.

The banks, which control trillions of dollars in assets, have until October to submit new “living wills” — detailed bankruptcy plans that eliminate concerns that taxpayers could be left on the hook if they fail. If those plans still are not “credible,” the regulators could eventually force the banks to sell off units or close lines of business.

These living wills are a critical requirement of the 2010 financial-reform legislation, Dodd-Frank, aimed at preventing a repeat of the taxpayer bailouts that took place during the 2007-2008 financial crisis. Congress demanded that big banks regularly submit detailed contingency plans.

But regulators found various problems with the plans submitted by Bank of America, Bank of New York Mellon, JPMorgan Chase, State Street and Wells Fargo.

The rejection will probably add fuel to the debate over whether U.S. banks are still too big to fail. The issue has taken center stage in the presidential campaign of Bernie Sanders, the senator from Vermont who has called for breaking up the big banks.

“This announcement is a very big deal. It’s scary,” Sen. Elizabeth Warren (D-Mass.) said in a statement. “And it means that, unless these banks promptly address the concerns identified by the regulators, the government must push these banks to get smaller and less complex.”

Regulators found shortcomings with Bank of America’s plan, for example, to dismantle its portfolio of derivatives, financial instruments investors can use to make bets. JPMorgan, the country’s largest bank, does not have a credible plan for keeping money flowing through its businesses during a bankruptcy, the regulators said.

“Obviously, we were disappointed,” Marianne Lake, the chief financial officer of JPMorgan, said during a conference call with investors Wednesday. “The most important thing is that we work with our regulators to understand their feedback in more detail. And we are fully committed to meeting their expectations.”

JPMorgan’s chairman and chief executive, Jamie Dimon, added that the bank has consistently worked to meet federal regulators’ demands in the years since the Dodd-Frank financial-reform law was adopted.

“We’re trying to meet all the regulations, all the rules and all the requirements,” Dimon said. “They have their job to do, and we have to conform to it.”

The banking industry sought to soften the findings, arguing that Wall Street today is stronger than it was before the financial crisis.

“No financial company should be considered too big to fail,” said John Dearie, acting chief executive of the Financial Services Forum, a banking industry group. “It is in the best interest of the industry that all large institutions have credible resolutions plans and, with that in mind, institutions will continue to work to address the technical shortcomings identified in this round of regulatory feedback.”

Bank of America, Wells Fargo, State Street and Bank of New York Mellon said they were committed to addressing the issues identified by regulators in the review.

Beyond the living wills, regulators are facing fresh threats to other measures put in place to respond to the financial crisis. For instance, regulators have attempted to identify financial firms, apart from banks, that could pose a threat to the economy. These firms have traditionally received little government scrutiny, but after the massive insurance company AIG nearly collapsed in 2008 and required a $182 billion taxpayer bailout, lawmakers called for stricter oversight of this portion of the financial industry.

So a government panel has labeled four firms — AIG, Prudential, General Electric’s financing arm and MetLife — as “systemically important financial institutions,” subjecting them to tougher government rules.

But GE is arguing that it no longer qualifies for the designation because it has shrunk its balance sheet. And MetLife, which was founded in 1868 and has a global footprint of 100 million customers and a market capitalization of $48 billion, filed a lawsuit that threatens the entire process.

This month, U.S. District Judge Rosemary M. Collyer overturned the company’s too-big-to-fail label and challenged the process the government used. The Treasury Department is appealing the ruling, which experts have said could hobble this portion of the financial-reform law.