With Dodd getting support from Senate Environment and Energy Chairman Barbara Boxer (D-Calif.), fellow Senate Banking panel member Sen. Bob Corker (R-Tenn.) arrived on the floor with some calming words.
"We can do this if everybody would calm down and if everyone would quit exaggerating how bad things are," Corker said.
Corker, who has been at the center of negotiations with Dodd before talks broke off in early March, said he met with the ranking member of the Senate Banking Committee Richard Shelby (R-Ala.) today and that "there's a strong, strong, strong desire to reach a bipartisan agreement."
Lawmakers could sit down and reach a bipartisan agreement on a bill and bring it to the floor within 10 days, Corker said.
"I relish the fact that we came so close and I think we can get there again," Corker added. "Let's just finish what we started."
Corker said he would prefer that the major points of the measure be mostly worked out before going to the floor.
Changes include examining loopholes added into the legislation by the Treasury Department and the FDIC that could lead to bailouts, Corker said.
"Some things could be tightened up and I think we can do that in five minutes, Corker said.
Dodd quoted FDIC chief Sheila Bair saying the measure makes a taxpayer-funded bailout "impossible" and any language in the bill that could allow for bailouts was eliminated.
Dodd reiterated that his door has been open to work on this bill for more than a year and if changes or tightening needs to be done then he's willing to continue discussions.
Earlier Thursday, McConnell said it's clear that both parties agree that action must be taken but "the bill our colleagues across the aisle are insisting on as a remedy is seriously flawed."
"The good news is, the bill can be improved, and both sides have expressed a willingness to make the changes needed to ensure without a doubt that this bill wouldn't allow future bailouts of Wall Street banks," McConnell said on the floor Thursday.
Several Republican staffers told reporters on Thursday that the bill does allow for bailouts -- with the set up of a $50 billion fund -- and that they are looking to make any necessary changes. The staffers wouldn't outline specifics on what they wanted in the bill.
The measure, which could reach the floor next week, not only ends taxpayer-financed bailouts but allows institutions to fail, forces creditors to pay for losses and requires asset liquidation, Dodd said.
We are "requiring these institutions to put up money in advance so that if they fail they end up paying for the cost of unwinding, who would object to that? Who's objecting to this?," Dodd said about a multi-billion dollar fund to be used in case future problems arise.
It's clear that big banks are opposing the bill because they don't want to pay to establish the "unwinding" account, Dodd said.
"We don't work for the big banks, we work for the American people to ensure this doesn't happen again," Dodd said.