"Congress is not – nor should it be – in the business of legislating the approval or disapproval of a construction project," Senator Angus King, an independent from Maine, said in a news release.
With the 100-member Senate one vote short of the needed 60 to pass a version of a bill that sailed through the House of Representatives last week, supporters including Democratic Senator Mary Landrieu lobbied for more support.
Construction of TransCanada Corp's Keystone XL pipeline has broad support in Louisiana, an oil-producing state, where Landrieu faces an uphill battle to win a new six-year term in a December run-off election.
Republican Senator John Hoeven of North Dakota, who introduced the bill with Landrieu, was asked by reporters at the Capitol on Tuesday if there were enough votes to pass it. "I think so," he said.
Hoeven told MSNBC the same thing earlier on Tuesday, adding: "We're at 59 votes confirmed. We've got a couple of maybes. I think there's one or two more that may join. So I think we have a good shot to get it."
King, who often votes with Democrats, had been seen as a possible swing vote despite his support of climate activism. He said he was "frustrated" by President Barack Obama's failure to make a decision on the pipeline that has been pending for six years.
The Senate is expected to vote as early as 6:15 p.m. EST on Tuesday.
Republicans generally support Keystone, which would transport more than 800,000 barrels of oil per day from Alberta to Nebraska, en route to the Gulf of Mexico.
But many environmentalists oppose the project, saying development of the oil sands would spike carbon emissions linked to climate change and that the oil could be sold abroad. Construction workers, unions, and energy companies say it would create thousands of jobs.
If Keystone does not pass on Tuesday, Hoeven plans to reintroduce the bill in January or February, when it has a better chance of a obtaining 60 votes in a Republican-led Senate. Next year Hoeven could also attach Keystone language to a wider bill that Obama would find hard to veto.
Obama raised new questions about the project during a trip to Asia late last week, saying it would not lower fuel prices for U.S. drivers but would allow Canada to "pump their oil, send it through our land, down to the Gulf, where it will be sold everywhere else."
Republicans and energy analysts said those comments likely mean Obama is leaning toward vetoing any Keystone bill.
TransCanada shares were down 20 Canadian cents at C$56.37 on the Toronto Stock Exchange on Tuesday.