Sen. John McCain, R-Ariz., agreed in an interview with Fox, saying, "Some of these banks have to fail."
Shelby went so far as to name names, pointing to ailing Citibank, already part-owned by the government following the financial industry bailout.
"Citi's always been a problem child," Shelby said on NBC's "Meet the Press."
Smaller banks have been failing at a rapid clip -- 25 last year. Last week the Freedom Bank of Georgia became the 17th to go under in the first 10 weeks of 2009.
The Obama administration is determined to save the nation's biggest banks, calling them too big to fail. Democrats say allowing them to fail would deepen the financial crisis, causing further harm to ordinary Americans.
"If they were to go down, the problem is, it's not just them. They take -- it's called, you know, collateral damage," Sen. Evan Bayh, D-Ind., told NBC. "A whole lot -- hundreds of thousands of blue-collar working men and women, other smaller financial institutions who were not involved in these bad decision-makings -- they'd all pay the price, too."
At its worst, that collateral damage could threaten bank customers' deposits. So many banks have failed, to be taken over by federal regulators, that the Federal Deposit Insurance Corp., which insures banks, had to assess new fees on healthy banks to avoid running out of money. The White House insists depositors' money is safe.
The goal of fixing the banks is to get them lending -- and Americans spending -- again.
"To restore the availability of affordable loans for families and businesses -- not just banks -- we are taking steps to restart the flow of credit and stabilize the financial markets," President Obama said in his weekly address, released Saturday.
Yet some economists insist that even freer credit would not persuade American consumers to return to their free-spending ways.
"We have come to an end of an era, this gilded age where we were spending and consuming and we had all of these fancy financials firms that seemed like they were perpetual money machine and it has crashed to an end," Harvard University economics Prof. Kenneth Rogoff told ABC News.
The end of that era could mean a permanent change in Americans' lifestyles, Kit Yarrow, a consumer psychologist at San Francisco's Golden Gate University, told ABC.
"Consumers have absolutely pulled back and they have become very focused on what is necessary and what is basic," she said. "So consumers have moved into a frugal new era."
A new, more frugal era could also mean a slower, longer recovery for the nation's economy, economists said.
One thing consumers have largely stopped buying is American cars. That has had a ripple effect on Chrysler and General Motors. Both are expected to seek billions of dollars more in a second round of federal bailouts.
Republicans also prescribed bitter medicine for the auto industry. McCain said President Obama should let GM go bankrupt. That advice came as a White House task force on the industry prepared to head to Detroit on Monday to meet with executives at Chrysler and GM.
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