The Senate voted 63 to 32 to take up the bill, which would end the State Department's six-year review of the 1,179-mile Canada-to-Texas pipeline and authorize its construction.
Ten Democrats and one independent joined all of the chamber's Republicans in backing the bill -- suggesting there are enough votes to approve it, a major milestone for a bill that had cleared the House
but stalled in the Senate in previous years.
Its passage is a goal
for new Senate Majority Leader Mitch McConnell, R-Kentucky, who has made it the first bill the now Republican-controlled chamber has taken up.
But the pipeline's supporters will need 67 votes -- a two-thirds majority -- to override an Obama veto. The President has said he would like the decision left in the hands of the executive branch, rather than handed over to Congress.
The push to build the pipeline got a boost Friday when the Nebraska Supreme Court OK'ed its route through the state, removing a legal case that the Obama administration had said it wanted to see play out before issuing a decision.
The Senate is likely to consider amendments to the bill this week and next week, with a final vote coming sometime around Obama's State of the Union speech.
The Keystone bill's sponsor, Sen. John Hoeven, R-North Dakota, told "Fox News Sunday" this weekend that he hopes the amendment process will attract more Democratic supporters to the bill.
"Right now we've got about 63 [votes]," Hoeven said. "But we're going to the floor with an open amendment process, trying to foster more bipartisanship ... so that we can pass this measure and other measures and either override the veto or attach the bill to other legislation that will get 67 votes."
One Democrat said on the program that he doesn't expect that to happen.
Sen. Chris Coons of Delaware said, "It's clear that there will not be a veto override."