Updated

Senate Majority Leader Harry Reid said Tuesday he's "very confident" that President-elect Barack Obama's request for the second half of the $700 billion financial bailout with pass the Senate.

"Do I have the votes? I think we'll get the necessary votes, yes," Reid said after meeting with Obama and other Senate Democrats Tuesday afternoon. "I feel very confident about that."

But Obama's campaign to win support for the release of the remaining $350 billion could still prove challenging, as many lawmakers think the money has been mismanaged.

Adviser Larry Summers met with Democrats on the Senate Finance Committee Tuesday morning, 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.

The incoming administration is banking on the Senate 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, which was made Monday by President Bush. A vote could come as early as Thursday.

But Obama's decision to tackle both a controversial new economic stimulus package and the second half of the bailout money even before he enters office could make for a chilly honeymoon.

Democratic Sen. Ron Wyden, Ore., left the meeting with Summers Tuesday saying he's still concerned about distributing the money and that he hasn't decided how he'll vote. He said the Bush administration mismanaged the money so far, leading him to be wary about approving any more of it.

Committee Chairman Max Baucus, D-Mont., said new conditions must be attached to the money.

"If the conditions are substantial enough, I'll support it," he said.

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's transition team prepared to dispatch top aides to meet with Senate Republicans this week in anticipation of a possible vote Thursday on whether to release the money from the embattled Troubled Asset Relief Program.

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.

Republicans on the House Financial Services Committee also urged Democratic Chairman Barney Frank on Monday night "in the strongest possible terms" to postpone a debate on the bailout package.

"Karl Marx famously observed that history repeats itself, first as tragedy and then as farce," GOP lawmakers said in a letter to Frank. "And it appears this Congress is trying to prove Marx correct. The original TARP was considered and enacted in a panicked rush to judgment. We are again moving far too quickly in considering whether to approve the expenditure of hundreds of billions of taxpayer dollars."

Congress has 15 days to act on the request for the funding.

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 they would ultimately need 67 votes to override a likely presidential 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 Senate Banking Committee Chairman Chris Dodd, D-Conn., 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.

House Speaker Nancy Pelosi released a statement Monday saying the House will vote this week on separate legislation from Frank ensuring more accountability to the distribution of the money.

But that could be a symbolic vote, since Obama might already have the bailout money by the time such legislation moved to the Senate -- if it moved to the Senate.

Rather, Democrats are seeking a "letter of assurances" from Obama's economic team spelling out conditions they will impose on the rest of the bailout money by the time the measure comes up for a vote. Some of those issues were addressed in Summers' letter to lawmakers on Monday.

Summers proposed strict oversight on the distribution of the money as well as limits on executive compensation and dividend payments for firms that accept the government assistance.

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