Democratic senators, emerging from talks with Obama's top economic advisers, said the administration of President George W. Bush was expected soon to ask Congress to release the mammoth fund's remaining $350 billion.
Like Obama, the senators complained that much of the money had been poorly spent. Meanwhile they welcomed changes to an enormous stimulus package that the president-elect insists is essential to avert economic disaster.
In an interview on ABC program "This Week," Obama said he was "disappointed" with the evolution of the so-called Troubled Asset Relief Program (TARP), which was approved by Congress last October in an atmosphere of acute crisis.
Angry Democrats argue that banks have pocketed the money without offering customers new credit, or have reduced competition by snapping up other banks, or have extended lavish bonuses to senior executives.
Obama said the second TARP instalment should focus on helping families at risk of losing their homes and small businesses trapped in the credit squeeze.
"And I think that we can regain the confidence of both Congress and the American people that this is not just money that is being given to banks without any strings attached and nobody knows what happens, but rather that it is targeted very specifically at getting credit flowing again to businesses and families," he said.
Bush's outgoing administration is coordinating with Obama's team to file a request for Congress to release the rest of the TARP fund before the new president takes office on January 20.
The request is expected to come in the "coming week," Kent Conrad, chairman of the Senate budget committee, told reporters after the meeting with Larry Summers, the incoming head of Obama's National Economic Council.
Wholesale changes are expected in terms of how the Obama administration will spend the money, with a view to making the process more transparent and better targeted, Democratic senators said.
"The Obama administration wants to rebrand this exercise. They realize it's been terribly mismanaged," said Christopher Dodd, chairman of the Senate banking committee.
The senators meanwhile welcomed assurances from Summers about the planned $775-billion stimulus package, which Obama said Saturday would save or create four million jobs and prevent a years-long recession.
Following Democratic criticism of individual and business tax cuts that were included to mollify Republican opponents, Conrad said: "It is very clear that they've listened and heard and are working to respond."
Democrats want Obama to keep his focus on an infrastructure spending spree and to raise the stimulus money intended for renewable energy tax breaks and unemployment insurance.
However, Republicans made clear they would oppose any move to reduce the role of family and corporate tax cuts, which Obama has said will comprise 40 percent of the total package.
Grumbling about its impact on the US budget deficit, which congressional watchdogs say will top one trillion dollars this year, House of Representatives minority leader John Boehner said the entire package should be rethought.
"Why couldn't we tax less and spend less as we put this package together?" he said on CBS television's "Face the Nation."
But on CNN, House Speaker Nancy Pelosi said the package "might" exceed $775 billion , and called for a repeal of tax cuts for high earners pushed through by Bush and the Republicans, to help offset its deficit impact.
Democratic Senator Charles Schumer said the stimulus bill could be ready for Obama's signature by February 13, and the president-elect promised to work closely with Congress in the days ahead.
"We're not trying to jam anything down people's throats," Obama told ABC.
But he stressed that "the sooner a recovery and reinvestment package is in place, the sooner we can start turning the economy around."
"We can't afford three, four, five, six more months where we're losing half a million jobs per month."