When Orszag deferred to Summers or Treasury secretary nominee Timothy Geithner for answers about those programs, Nelson said that wasn't good enough.
"It is my understanding that by Thursday, or maybe Friday, we're going to vote on whether or not to expend an additional $350 billion of TARP money," he said. "I think in this era of freshness and transparency that the new administration would want to come forth with detail(s) instead [of] this mumbo jumbo that's going on."
Three Democrats emerging from the meeting with Summers said they'd need more assurances from the incoming Obama administration about how that money would be spent, how it would be tracked and what conditions would be imposed on the institutions that take it.
"We need to have a better understanding and a better idea of how those dollars are going to be spent and where they're going to go. We haven't gotten a good idea in the past," said Sen. Blanche Lincoln, D-Ark.
"The letter was fine," she said of the message Summers sent to Congress Monday, laying out how the Obama administration would seek to keep track of the second $350 billion. "But there were no specifics in that letter."
Another concerned voice was that of Senate Finance Committee Chairman Sen. Max Baucus, D-Mont.
"Most senators are very concerned that the first 350 was spent unwisely and that if there is a second 350, it is spent more wisely," Baucus said. "I'm looking at the conditions. If the conditions are quite significant, then I'll support it. But I have to see the conditions."
Oregon Sen. Ron Wyden, one of the few Democrats in the Senate to oppose the initial TARP legislation, said there is a tremendous amount of "voter angst" with regard to TARP. Many people, he said, view the bailout as an enormous "bait and switch."
He said the Bush administration did not follow through on assurances it made regarding oversight. But he dodged questions about whether assurances from the Obama administration would be sufficient to secure the money.
Those concerns will certainly affect the crafting of the stimulus package.
Many Democrats initially expressed skepticism with Obama's recipe for the stimulus package, saying it focuses too much on tax measures and not enough on direct investment by the government in aid to states and infrastructure spending on things like roads and bridges.
Several of the Democratic skeptics appeared satisfied that they have convinced Obama to drop the $3,000 tax credit he had planned for businesses that hire new employees. But dropping that provision will surely frustrate some Republicans who had voiced optimism about the stimulus plan last week.
"I'm not going to get into details, but all along, the view has been that nobody had a monopoly on good ideas in this legislation," Summers told reporters after his meeting with Democrats.
ABC News' Huma Khan, Dean Norland, Sunlen Miller and The Associated Press contributed to this report.