After hearing a powerful and eloquent push directly from the lips of incoming President Barack Obama, Senate Democrats appear poised to put their faith in the new administration and abandon demands for specifics on how it would handle another installment of Wall Street bailout funds.

“I feel much better” about supporting the financial industry rescue, Sen. Claire McCaskill (D-Mo.) said after listening to Obama’s nearly hourlong pitch at the Democrats’ weekly policy luncheon on Tuesday.

Senate Majority Leader Harry Reid (D-Nev.) emerged “confident” that he could muster the 51 votes needed to beat back a GOP-led effort to pass a resolution of disapproval, which would prevent the Treasury Department from accessing the remaining $350 billion.

“We must approve that for a number of reasons, the most important of which is the ability to do something about housing,” Reid said. “We can all look back and talk about how the first $350 billion was not spent, but it’s very clear that there’s going to be a lot of money spent to help the housing industry.”

Reid said the vote on the money would come before Sunday, while aides said it is likely to occur on Thursday or Friday.

Senate Banking, Housing and Urban Affairs Chairman Chris Dodd (D-Conn.) acknowledged that Democrats have backed off on their demands that Obama economic advisers send them a detailed letter on how they would introduce more oversight, accountability and transparency into a program that most lawmakers believe has been terribly mismanaged by the Bush administration. Congress approved the first installment of $350 billion in October.

Dodd said he scrapped plans to exchange letters of understanding with Treasury Secretary appointee Timothy Geithner, after Lawrence Summers, Obama’s choice to head the White House’s National Economic Council, sent a broadly worded letter to House and Senate leaders in both parties on Monday. The Summers letter was privately panned by Democrats as not going into enough detail about the changes Obama and Geithner plan for the program.

“They decided to do it differently,” said Dodd, who promised hearings in the next few weeks to elicit the specifics that Senators want. Holding hearings, he said, “makes more sense than, with 72 hours, trying to fashion something in great detail between now and then before a vote. That invites a delay on all of this at a time when I think urgency is needed.”

Rank-and-file Democratic Senators were cautious about saying that Obama had hit the mark, even as they praised his appeal and noted that he had embraced Congressional efforts to ensure greater oversight and accountability of the bailout.

Sen. Debbie Stabenow (D-Mich.) said she was not completely certain how she would vote on the forthcoming resolution of disapproval, but that Obama, as the closer on the deal, made a powerful case.

“I think he did a lot of closing today. … I would say there is no better closer,” Stabenow said.

While he didn’t offer to provide more specifics on what he will do, Obama embraced the rigorous oversight required under a bill written by House Financial Services Chairman Barney Frank (D-Mass.), Stabenow said. The measure is making its way through that chamber.

Still, some Senators remained highly skeptical.

“They made a strong case, and at the same time there’s a very strong distaste for what’s happened so far,” Sen. Sheldon Whitehouse (D-R.I.) said. “I’d just be making wild guesses as to whether the strong push or the strong distaste will win out.”

Senate Republicans, who did not get a personal appeal from Obama during their weekly lunch, said they were not impressed with Summers’ assurances that Obama would change the way the program is run.

“I think many of my Members think Summers’ letter is not enough to get their support,” Senate Minority Leader Mitch McConnell (R-Ky.) said, adding that Obama “wants very much to have Republican support, [and] I’m suggesting a way to do that is more specificity at how this money will be targeted.”

Even moderates seen as more likely to vote with the Democrats said they were wary of handing the new administration $350 billion with no new strings attached.

“I have a lot of reservations on voting for an additional release of funds given the ineffectiveness of the first installment,” Sen. Susan Collins (R-Maine) said.

Jessica Brady contributed to this report.