Summers assured Democratic senators late last week that the incoming administration would ensure that more of the money is used to help homeowners and promised better accounting of the cash.
A vote on the Troubled Assets Relief Program request could come as early as this week, in time for Obama to begin spending it when he takes office next Tuesday.
"My colleagues in the Senate will not vote for any additional funds unless they're assured by the Obama administration that these provisions will be a part of it," Dodd told "GMA."
And Obama has promised Congress he will do just that.
"Barack Obama ... has said he is going to rebrand this entirely and demand accountability," Dodd said.
Democrats and Republicans have been angered over the Bush administration's inability to detail how the first $350 billion of the TARP has been spent and how little of it went to help homeowners avoid bankruptcy.
"It's disgraceful. We're losing 9,000 homes a day in this country," Dodd told "GMA." "And the anticipation is, beginning in January, with some of these new mortgages that have been created earlier coming due, you may have as many as 8 million homes in this country being adversely affected."
"It's obviously been totally mismanaged by the Bush administration," he said.
Dodd said that bankruptcies affect more than just homeowners who can't pay the mortgage. "If your neighbor is in foreclosure, the value of your home will decline between 1 percent and 5 percent the very day that foreclosure occurs," he said.
The Bush administration defended its efforts to help homeowners on "GMA" today.
Housing and Urban Development Secretary Steve Preston said, "The first thing that needed to be done was to make sure that the financial system was solid because that's the system through which mortgages come."
Congress tried to provide some relief by creating the Hope for Homeowners program, intended to help 400,000 homeowners, but so far the program has attracted only 370 applications.
"This is a very small program right now in the context of a much bigger response," Preston said. "And whereas I think it's an important program and it can be tweaked to make it more effective, and Congress is listening hard on how to do that."
He also said that HUD and the Federal Housing Authority has arranged refinancing for 500,000 people.
"I think the government response has been massive and responsible," Preston said.