Senators struggled with last-minute objections from Republican Rand Paul, but have now passed the bill, which has gone to the House for its vote.
Federal funding for government services expired at midnight (05:00 GMT).
The 600-page plan proposes an increase in spending, by about $300bn (£215bn), on defence and domestic services.
If the plan is passed in the House of Representatives and signed by the president in the next few hours, the shutdown could be rescinded before the US working day begins on Friday.
But it is not clear how the House will vote, and how public services would be affected on Friday if the shutdown were to continue.
The federal Office of Personnel Management said government operations would “vary by agency” and employees should “refer to their home agency for guidance on reporting for duty”.
CNN is reporting that if the shutdown is not averted, government agencies will still be able to call their employees in for a half day’s work to make the shutdown go smoothly.
Employees deemed essential – including military personnel – are required to work regardless of shutdowns.
While the spending bill’s funding for the Pentagon has delighted the national security wing of the party, fiscal conservatives are up in arms about ramifications for the nation’s debt.
In a doom-laden speech, Senator Paul angrily charged his fellow Republicans with fiscal profligacy.
“I ran for office because I was very critical of President Obama’s trillion-dollar deficits,” he said.
“Now we have Republicans, hand in hand with Democrats, offering us trillion-dollar deficits.
“I can’t in all good honesty, in all good faith, just look the other way just because my party is now complicit in the deficits.”
This would be “the very definition of hypocrisy”, he added.
The 650-page spending plan was only unveiled on Wednesday night, so the finer details are unclear.
White House legislative affairs director Marc Short said the package would increase spending by “just shy” of $300bn. (Courtesy BBC)