Updated

President-elect Barack Obama is running into deep skepticism, even from his own party, as he tries to convince Congress to free up the remaining half of the $700 billion Wall Street bailout.

Senate Majority Leader Harry Reid said Tuesday he's "very confident" he can round up the votes needed in his chamber to approve Obama's request. But Republicans and Democrats gave a glimpse of their grievances with the program during a House hearing the same day.

Lawmakers complained that the management of the fund so far amounts to an unregulated giveaway of taxpayer dollars, signaling that Obama's decision to press for billions more in stimulus and bailout dollars early on will make for a rocky honeymoon.

"We're seeing now this thing transition ... into a grab bag where people can just reach in and get taxpayer money. As most of you know people are lining up to get this money," said Alabama Rep. Spencer Bachus, the ranking Republican on the House Financial Services Committee. "We're not informed, we don't have the facts, but we're told that we need to pass it. ... And that's not the way to do legislation."

Committee Chairman Barney Frank, D-Mass., who wants the money released, is putting forward a bill that would place new conditions on the remaining $350 billion in bailout funding, called the Troubled Asset Relief Program. He says the legislation will focus on ensuring foreclosure relief, curbing executive compensation and adding other restrictions.

Rep. Michael Capuano, D-Mass., said it's "insane" the distribution doesn't already have conditions for tracking the money that goes to banks.

President Bush requested the second half of the funding Monday on Obama's behalf, starting a 15-day ticking clock during which Congress has to act if they want to withhold the funding.

The incoming administration is banking on the Senate, though, to clear the request for the $350 billion, since the House is likely to deny the funding. Only one chamber needs to approve Obama's request, and a vote could come as early as Thursday. Sen. David Vitter, R-La., formally introduced the measure Tuesday.

But even some Democratic senators are disappointed with the way the program has been administered.

"It's a public relations nightmare," said Sen. Ben Nelson, D-Neb., who is wrestling with whether he would back Obama’s plan. "I can't explain to people how (the rescue money) is working. It's beyond a snake bite."

Senate Banking Committee Chairman Chris Dodd, D-Conn., underscored the desire of Democrats to "fundamentally change" how the government handles the relief money.

But he conceded it was a heavy lift to convince lawmakers to agree with Obama's approach, given the public outcry about the first wave of funds.

"This is not a popular vote," Dodd said. "If anyone thinks they're going to get a plaque or a parade back home, they're delusional."

Sen. Claire McCaskill, D-Mo., summed up the uphill challenge Obama faces within his own party as he travels to Capitol Hill to win allies.

"I call it the grocery store test. How far down the aisle can I get before someone yells at me? Most of the time, now, I don't even get to produce." And that section is by the store entrance, she said.

An outspoken Obama campaign supporter, McCaskill said she trusts Obama but, "We don't know enough about the first $350 billion. ... We have to be careful that in our haste to do something, we don't get sloppy. We did on the first one."

McCaskill, a former state auditor, is demanding to know if taxpayer money has been wasted and said she wants promises of "a full accounting" of how the initial $350 billion was spent.

Frank said his motto for his legislation is one borrowed from President Ronald Reagan: "Trust but verify."

In a closed-door meeting with Senate Democrats, Obama sought to allay fears about how the Bush administration spent the first wave of funds and explained his ideas for enhanced accounting mechanisms. Obama economic adviser Larry Summers also got to work Tuesday persuading skeptical senators to release the second half of the financial bailout. He met with Democrats on the Senate Finance Committee, after sending a letter to Democratic and Republican leaders the day before spelling out reforms that the president-elect intends to make for the distribution of the second half of the funding.

Senate Majority Whip Dick Durbin, D-Ill., said Tuesday that convincing the Senate to release the money "will be a challenge."

But he said Obama could win over skeptics since he will be in charge of administering the funds instead of the sitting president.

Obama does have allies in Democratic leadership, as well as Democratic members of the Finance Committee. And one key Republican, Sen. Judd Gregg, R-N.H., a fiscal hawk, is lobbying his side for support.

Obama's transition team prepared to dispatch top aides to meet with Senate Republicans this week in anticipation of a possible vote Thursday.

Senate Republican Leader Mitch McConnell, R-Ky., released a statement Tuesday saying taxpayers still don't have "assurances that this money will not be wasted or misused to play favorites."

"We'll hear from the incoming administration soon. They will have a receptive, if cautious, audience," he said.

The process for approving the money is complicated, and would require lawmakers supportive of Obama's request to vote against the measure that comes to the floor -- called a motion of disapproval. If they vote against the measure, the Obama White House gets the money. If they vote for the measure, then they are denying Obama that money.

Opponents to the release of the money would need 51 votes to deny the funds, and several sources said that seems achievable.

But Obama threatened to veto such a move Tuesday in his meeting with lawmakers, according to a Senate leadership aide. Opponents to his request would then ultimately need 67 votes to override a veto, which would be tougher. In other words, supporters of Obama's request need only round up one-third of the Senate to approve the money.

Obama's pick for treasury secretary, Timothy Geithner, has been working with Dodd on ways to reshape the program and in turn generate more support for the proposal.

The unpopular bailout has so far featured unconditional infusions of money into financial institutions that have done little to account for it.

Republicans in both chambers are skeptical about the second half of the bailout money, particularly because they think the recent use of some funding to bail out the auto industry signaled that the money is heading toward those with political clout rather than struggling financial institutions.

FOX News' Jim Angle, Trish Turner, Chad Pergram and The Associated Press contributed to this report.