The efforts propose additional bankruptcy conditions to benefit the 2,000 dealerships cast adrift by the two companies.
The Wall Street Journal reported talks were under way among automakers, members of Congress and cast-off dealerships to reach a compromise on the issue.
A majority of House members have co-sponsored a bill restoring the rights of cut-off dealers under state franchise laws, the Journal said, but Senate Majority Leader Harry Reid, D-Nev., said the matter isn't a high priority in his chamber.
Meanwhile, the White House said the legislation could harm manufacturers' restructuring using $60 billion in government funds.
"The decision to invest taxpayer dollars into these companies required all stakeholders to make difficult sacrifices," the Office of Management and Budget said in a statement reported by the Journal. "It would set a dangerous precedent, potentially raising legal concerns, to intervene into a closed judicial bankruptcy proceeding on behalf of one particular group at this point."