The industry has been pleading with US politicians for $25 billion in loans to stay in
business until spring following months of heavy financial losses and wide-ranging job cuts.
Democrats have demanded that the White House and US treasury provide the funds from a $700 billion finance industry bailout to support the automakers.
However so far they have resisted, saying the senate should allow the industry to use $25 billion in already existing Energy Department loans.
Later on Thursday, the White House said it could back a draft proposal aimed at finding a compromise solution.
A proposal by Carl Levin, a Michigan Democrat, and Christopher Bond, a Missouri Republican, would allow the ailing auto industry to use $25 billion Energy Department loans to address its current crisis.
"Their plan provides assistance from already-appropriated funds, and has strong taxpayer protections," said Dana Perino, a White House spokeswoman .
Reid said that the firms should come up with a new plan, involving restructuring of the firms, by the week of December 2, when US congress could hold another session to mull an emergency cash injection in the following week.
"In light of the importance of this issue to all of us, we have decided that the best way to proceed is to give the auto companies another opportunity to make their case."
Nancy Pelosi, Democratic speaker of the US House of Representatives, said that the chiefs of top car makers had so far not been clear on how they wanted to
restructure the industry for the future.
"Until we can see a plan where the auto industry is held accountable and a plan for viability on how they go into the future - until we see the plan, until they show the plan, we cannot show them the money," Pelosi said.
Al Jazeera's Rob Reynolds in Washington DC says it will be a "near thing" as to whether the car firms will manage to hang on until December or next year even if the plan is approved in what is becoming a desperate situation for many people and many businesses in the US.