AIG CEO Edward Liddy said in a letter to Treasury Secretary Timothy Geithner that the payments can't be stopped and that his "hands are tied."
Cummings admitted that the stimulus package was moved through Congress so quickly that there may be room for improvement going forward, including add-ons that would prevent failing banks and institutions from using government money to reward the same executives who were responsible for the company's failure in the first place, such was the case with AIG.
"We have to be very careful ... we don't allow these things to happen again," Cummings said.
"There are a lot of terrible things that have happened in the last 18 months, but what's happened at AIG is the most outrageous," Summers said this morning on ABC's "This Week With George Stephanopoulos." "What that company did, the way it was not regulated, the way no one was watching, what's proved necessary, it is outrageous."
Summers repeated the characterization several times on the morning talk show circuit.
Lawmakers, too, are furious at the payout of big bonuses at a company that has so far eaten up $170 billion in taxpayer money, and whose risky behavior has helped push the economy into one of the biggest financial crises in American history.
"The message here, I'm afraid, to any business out there that's thinking about taking government money, is let's enter into a bunch of contracts real quick, and we'll have the taxpayers pay bonuses to our employees," Senate Minority Leader Mitch McConnell, R-Ky., said on "This Week." "This is an outrage."
Sen. Russ Feingold, D-Wis., sent a letter to Treasury Secretary Timothy Geithner saying he "would like to know what legal options have been explored for canceling the bonuses or recouping the money from the recipients, and in particular whether the Administration has considered holding AIG executives accountable in court for any breaches of their fiduciary duties to the shareholders."
An angry Geithner called AIG chief executive Edward Liddy Wednesday, demanding he slash the bombshell bonuses.
"AIG'S hands are tied," Liddy replied. In a letter to Geithner yesterday, Liddy said he found the bonuses "distasteful" but he added, "These are legal, binding obligations" and "we must proceed with them."
Obama's top economics adviser agreed that despite committing $170 billion in bailout money to AIG, the government was limited in its power to stop the bonuses.
"This is an example of people at the commanding heights of the economy misbehaving, abusing the system," Rep. Barney Frank of Massachusetts said on "Fox News Sunday."
"I do think it's inappropriate for those people to stay in power at that company," Frank said.
AIG's Liddy was recruited last year by the Bush Administration to run the company, and the bonuses were negotiated before he arrived.
Cummings cites AIG's lavish corporate parties and historic losses and says Liddy should step down. He said he can't believe most of the bonuses are to retain the executives who have been leading AIG.
"It's like, OK, you got to help me screw you," Cummings said. "And by the way I'm going to take your money and I'm going to slap you with it. As I walk into this $1,500-a-night hotel to have fun."
Liddy will face soon more questions about the bonus backlash as well. He'll be in the hot seat at a House hearing this week to explain how American taxpayers ended up paying millions more to executives who have already cost them billions.
ABC News' Matthew Jaffe and The Associated Press contributed to this report.