Last-minute negotiations are expected to take place in Washington between Democrat and Republican lawmakers to try to agree a new budget.
If they fail to reach a deal by midnight (04:00 GMT Tuesday), the US government will be forced to close all non-essential federal services.
More than 700,000 staff could be sent home on unpaid leave, with no guarantee of back pay once the deadlock is over.
The shutdown would be the first in the US for 17 years.
One of the key reasons for the political stalemate has been President Barack Obama's healthcare law, popularly known as Obamacare.