US Republican leaders offered the White House a proposal to temporarily extend the debt limit, appoint budget negotiators and begin talks to reopen government.
No final decisions have been made, according to a spokesman for the Speaker of the United States House of Representatives, John Boehner.
The conversation with White House was "useful and productive," and the President and Republican leaders agreed communication should continue throughout the tonight, he added.
The US shutdown is but a precursor to a much bigger problem - in a couple of weeks the government, shutdown or not, will run out of cash.
Landmarks across the US have closed as the Congress failed to reach a deal over the budget.