Mr. Pataki said the government could be kept running with stopgap bills, though schools would have a harder time predicting aid.
While the stopgap bills are keeping the Government operating, they generally reduced spending at agencies, although the details of how the cuts are apportioned are difficult to calculate.
But with a vote scheduled next week on an impeachment inquiry, they may have to buy more time with another stopgap bill.
Speaker Newt Gingrich held out the possibility that Congress may seek a series of stopgap bills, known as continuing resolutions.
The current stopgap bill expires next Tuesday.
Bush later vetoes the stopgap bill that was approved the previous night.
The earlier stopgap bill, which was passed in September and expired at midnight, allows for no more than a 10 percent cut in spending.
But the White House said President Bush, in an attempt to force Congress to pass a budget, would not sign the stopgap bill.
Such stopgap bills are known as continuing resolutions because they continue financing Government operations until a regular appropriation bill containing funds for an agency or program can be passed.
Congress could pass a stopgap bill to continue spending at current levels under existing rules for a few months or for a year.