A deal seemed likely until Sen.
That now sets up a chance for both sides to offer amendments that will compete for 60 votes - the threshold to advance legislation in the Senate.
If the Senate approves it, the bill will next move to the House, where a vote was planned and passage was expected but not assured amid resistance in both parties.
The deal would hike defense and domestic spending by more than $400 billion and raise the debt limit.
But the bill has hit some unexpected snags as Congress races toward the deadline.
On Thursday, however, Senator Rand Paul (R-Kentucky) used Senate procedures to delay the vote on the proposal until after midnight - after the deadline imposed by the most recent continuing resolution, passed at the end of the January shutdown.
The funding measure will still need to be passed by the House if the Senate passes the deal.
The 71-to-28 Senate vote, which took place just before 2 a.m., capped a topsy-turvy day that featured filibuster threats, fuming congressional leaders, and frenzied vote counting.
US Senate passes funding bill in bid to end shutdown
The California Democrat spoke for just over eight hours, urging Republicans to bring a bill to the floor that would address DACA . Obama-era guarantees for those immigrants were cancelled by US President Donald Trump and are set to become invalid next month.
On the Senate floor, McConnell attempted to move forward with the vote via a parliamentary procedure but was rebuffed by Paul. The House had already voted on a short-term funding measure, known as a continuing resolution (CR), earlier this week that also expired March 23, but provided a boost in funding to the Pentagon through September.
He complained in an interview with Fox News: "I'm not advocating for shutting down the government".
"If you're against president (Barack) Obama's deficits, but you're for the Republican deficits, isn't that the very definition of hypocrisy?" he boomed, adding that he wants his fellow lawmakers "to feel uncomfortable" over the impasse. Speaking to the New York Times, Rep. Mark Meadows, chairman of the House Freedom Caucus, said, "It was pretty much a smorgasbord of spending and policy that got added to this ... normally, people who eat at smorgasbords all the time are not the healthiest".
Speaking on the Senate floor, Paul said United States taxpayers "are getting stuck with the bill" as spending levels beyond the amount of revenue are allowed. The breaking of ranks by the less moderate members of the GOP and the alienation of the Democrats could make it hard for the plan to gain the needed total.
Some fiscally-minded Republicans disapproved of the bill's increased spending, among them Sen.
Mr Trump also wrote that the administration was forced to increase spending on "things we do not like or want" and negotiations will "start now!" on an immigration measure that he and Democrats have been battling over for months.
In a February 8 press conference, Pelosi said she wasn't trying to whip votes against the bill.
And liberal stalwarts including top House Democrat Nancy Pelosi were also in revolt because the deal does nothing to protect young undocumented immigrants from deportation.
Friday's vote in the House culminated in a weird standoff, with Democrats holding back the vast majority of their votes to show just how many Democratic votes Republicans needed to pass the bill.