Bankers may have fallen out of love with the Obama administration, but they're still hoping that its next Treasury Secretary will solve some of their problems.

Now that President Barack Obama has been re-elected, current Treasury Secretary Tim Geithner is expected to step down. On Thursday, the chief executives at two of the nation's biggest banks said Geithner's successor should focus on eliminating economic uncertainty and on helping the industry handle international regulations, including changing capital requirements.

"We need to spend time managing all the international rules" that big banks are facing, U.S. Bancorp (USB) CEO Richard Davis said at a panel discussion on Thursday.

Davis praised Geithner for doing "a great job," but added that his successor will have to ensure that international regulations do not overwhelm U.S. banks, or make them scale back their operations.

"We also have to make sure that we don't sacrifice national competitiveness," he said, addressing the annual meeting of The Clearing House Association in New York.

James Rohr, the CEO of PNC Financial Services Group (PNC), said his first priority for a new Treasury Secretary would be eliminating economic uncertainty, including many businesses' concerns over the fiscal cliff, health care reform and taxes. Such worries are keeping many bank customers, especially small businesses, from borrowing.

"That uncertainty piece is really holding the economy back," Rohr told the panel.

Both executives told American Banker after the panel that they expected current White House Chief of Staff Jack Lew to get the job. Davis said Lew's already-close working relationship with President Obama would benefit him in such a position. Davis also praised Erskine Bowles, who co-chaired the President's National Commission on Fiscal Responsibility and Reform, and BlackRock's Larry Fink as potential candidates who would do well as Treasury Secretary.

Regulations and economic uncertainty are two of the thorniest issues facing the biggest banks, but much of the panel was also devoted to discussing something much more ineffable and possibly more difficult to repair: reputation.

"There are no allies for banks. There's nobody speaking on behalf of banks," Davis said during the panel. "We still have to build a reputation story."

Both Rohr and Davis are in relatively enviable positions — their banks are large without being in the top rungs of the megabanks, and without facing some of the headline-splashing scandals that have dogged JPMorgan Chase (JPM), Citigroup (NYSE: C) and Bank of America (BAC). But Davis and other panelists expressed frustration with the industry's inability to improve its overall standing four years after financial crisis.

"Everything that goes wrong in finance is a bank. The mortgage brokers caused the crisis, but it's the banks" that get blamed, said Eugene Ludwig, the head of Promontory Financial Group. "Many of these issues are not banking issues."

Rohr was somewhat resigned to the industry's reputational issues.

"I think we've just got to do our job. There's no advertising campaign, there's no gift-giving program" that can help, he said, before extolling some of the industry's philanthropic efforts. "That's kind of lost in this reputational issue around mortgage. You've got to just kind of do our job and get out of it."

Davis said that banks wanting to repair their reputation should play up their similarities to smaller companies, with their generally tight-knit relationships in the communities where they work.

"You've got to make it all more local," he said.

The panel was moderated by American Banker editor-at-large Barbara Rehm. Patrick Parkinson, also of Promontory and formerly of the Federal Reserve, also participated.

The two chief executives also weighed in on how they are handling the new regulations they are facing from the Dodd-Frank Act and the Basel III capital requirements.

"There's just an enormous amount of regulatory everything. Dodd-Frank touches every single part of the company," Rohr said. "We've had three different committees added to our board that deal with how we implement things."

He said that a lot of Dodd-Frank's reforms were "appropriate," but that complying with them all at once is complicated.

"We just have to deal with all of these changes, and I don't think that any one of them is terrible, it's just a lot at once."

Davis also reiterated the frequent industry warning that regulation will make it too costly for banks to do business with many customers.

"Banking services will become less and less available to more and more people. And we're not threatening, we're not being mean, we're not trying to make a point. But now you have credit risk and all those other risks" to worry about, he said. "That next scream you'll hear from Congress a couple of years forward will be wondering where the banks are."

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