The concerns appear unlikely to force President Barack Obama to push out his Treasury secretary, for whom he voiced renewed support today. But the worries could undermine the Obama administration's efforts to keep Congress on board for a more comprehensive approach to propping up the financial system.
Today, two members of Congress -- Rep. Connie Mack, R-Fla., and Rep. Darrell Issa, R-Calif. -- became the first to call on Obama's Treasury secretary to resign.
"Secretary Geithner either didn't know about the bonuses, and was grossly negligent, or he did know and failed to bring this to the president's attention," Issa, the top Republican on the House Government Reform Committee, said in a statement. "Either way, the end result has been a significant waste of taxpayer dollars and he should take immediate responsibility and resign."
House Minority Leader John Boehner, R-Ohio, stopped just short of joining their calls, telling a radio interviewer that Geithner is "on thin ice." He said the administration needs to provide more details of "what the administration knew and when they knew it."
Several Democrats, while continuing to stand behind Geithner publicly, are serving notice that their patience has limits.
Asked if he supports Geithner, Rep. Michael Capuano, D-Mass., said: "At the moment, yeah. I mean, I have questions like anybody else, but let's be serious. He's still new on the job, he hasn't been able to get anybody else appointed or actually confirmed by the Senate. So, I think it's a little too early to pass that judgment."
Rep. Paul Hodes, D-N.H., who serves with Capuano on the House Financial Service Committee, offered similarly lukewarm support: "I think Secretary Geithner is doing generally a good job, and I'm hoping that he's learning quickly how difficult the job he faces is."
They join a growing number of Democrats who are voicing concerns. Sen. Ron Wyden, D-Ore., is complaining that Obama's economic team is sending mixed messages.
"The president goes out and says this is not acceptable, and then some backroom deal gets cut to let these things get paid out anyway," Wyden told the AP. "They need to put this to bed once and for all."
The Treasury Department declined to comment today on congressional skepticism, citing the president's comment.
Though Geithner declined to appear at a House subcommittee hearing on AIG today, he was a presence in the hearing room -- and not in a positive way.
"I was remarkably disappointed that Treasury Secretary Tim Geithner declined to testify at today's hearing, considering the primary role he played in the governmental intervention into AIG," said Rep. Tom Price, R-Ga., arguing that the country needs "an exit strategy" from bailouts.
Geithner will appear at another House Financial Services Committee hearing next Tuesday, where he's expected to get a grilling from lawmakers on AIG and other matters.
President Obama today issued a strong defense of Geithner, saying he has "complete confidence" in his leadership.
"There has never been a secretary of the Treasury, except maybe Alexander Hamilton, right after the Revolutionary War, who's had to deal with the multiplicity of issues that Secretary Geithner's having to deal with, all at the same time," Obama told reporters in Washington. "And, you know, he is doing so with intelligence and diligence. Nobody's working harder than this guy. You know, he is making all the right moves in terms of playing a bad hand."
Several congressional aides said members of Congress remain unlikely to press for Geithner's ouster in large numbers. At the very least, according to one Democratic leadership aide, members are likely to wait for Geithner to present his comprehensive bank bailout plan before passing judgment.
But Geithner's 51-day tenure at Treasury has been rocky from before it started. Errors he made on his tax returns presented an early challenge for the Obama transition team, though the Senate confirmed him despite the fact that he owed back taxes.
Geithner's initial bank bailout plan was widely panned for being short on specifics. And though Geithner has said he only learned about the AIG bonuses last week, he was closely involved in the initial AIG bailout as head of the New York Federal Reserve.
Obama aides have indicated that Geithner tried and failed to get the bonuses cancelled last week. But several lawmakers expressed exasperation with the notion that nothing could be done to stop the money from being paid out.
"It is ridiculous to stand on these contracts as justification for paying the bonuses," Hodes said in today's hearing.
The outside world is taking note of the heat. The futures trading Web site Intrade last week had the odds of Geithner leaving by the end of December around 22 percent; as of this afternoon, the odds had jumped to about 35 percent.
ABC News' Matthew Jaffe contributed to this report.