Democrats struggle with a president who says he wants to compromise but then is reined in by his own staff, while Republican leaders are loath to guess at his intentions.
A group of bipartisan lawmakers emerged as the negotiators behind a potential deal to end the gridlock and reopen the government.
Lawmakers remained mired in partisan disputes as Senator Mitch McConnell said he would move ahead with a vote on a temporary spending bill by 1 a.m. Monday.
The House and Senate reconvened for a rare Saturday session, hoping to find a way to restart the flow of funds after much of the federal government shut down, while Republican and Democratic leaders blamed each other for the stalemate.
The vast machinery of the federal government began grinding to a halt, but much of the bureaucracy will stay in motion for a while.
With the government shut down and the two parties faulting each other, senators from both parties were looking for an agreement to end the crisis.