President Donald Trump is vowing to veto any bill that doesn't fund a border wall, and Congressional Democrats are refusing to pay for it.
A shutdown would affect more than 800,000 federal workers. At agencies such as NASA, some 95 percent of employees would be furloughed.
Transportation Security Administration agents could end up working without pay over the busy holiday weekend.
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About 75 percent of the federal government would not be affected by a shutdown.
Those agencies, including the departments of Defense and Veterans Affairs, are already funded for the full fiscal year.
The Senate was expected to reject the House measure because Democratic votes are needed and McConnell showed little interest in changing the rules — as Trump proposed — to allow a simple majority for passage.
Both the House and Senate packages would extend government funding through Feb. 8, all but guaranteeing another standoff once Democrats take control of the House in the New Year.
“There are a lot of us who want to avoid a shutdown,” said Kansas GOP Sen. Pat Roberts. “I’ve been through about five of them in my career. None of them have worked in terms of their intent.”
The Associated Press contributed to this report.