In their statement, Landrieu and Hoeven said the legislation has the support of 11 Democrats and all 45 of the Senate's Republicans, a total of 56 of the 60 that will be needed. "A vote on the bill is expected in the coming days," they added.
The obvious targets for additional support include six Democrats who voted in favor of a non-binding proposal 13 months ago that expressed general support for the project: Sens. Michael Bennet of Colorado, Bob Casey of Pennsylvania, Chris Coons of Delaware, Tom Carper of Delaware, Tim Johnson of South Dakota and Bill Nelson of Florida.
Among the group, Johnson and Coons indicated Thursday they do not support the legislation to require construction.
In an interview, Johnson said he wants to know President Barack Obama's position. Ian Koski, a spokesman for Coons, said the lawmaker "believes the law makes clear that it's up to the (Obama) administration to make permitting decisions like this one," and not up to Congress.
Casey noted he has twice before voted in favor of the project, and said it was "probably a good guess" to assume he will do so again.
Carper said he is undecided, and intends to meet with Landrieu, Hoeven and others in the coming days.
Nelson and Bennet could not be reached for immediate comment.
The proposed pipeline would carry oil from Canada to the United States, where it eventually would reach Gulf Coast refineries. Supporters say it would create thousands of jobs and help the United States get closer to a goal of energy independence. Opponents include environmentalists who say the project wouldn't create much permanent employment once it was finished, and say it would reinforce the nation's use of an energy source that worsens global warming.
The legislation is the latest response in Congress to the Obama administration's recent announcement that it was delaying a decision on the pipeline indefinitely, citing a Nebraska court case relating to the project.
The House has voted previously to approve construction of the pipeline.
The White House has not taken a formal position on the legislation, although Democratic officials in the Senate as well as Republican lawmakers say they expect Obama likely would veto it if it reaches his desk.
In a sidebar dispute, some Republicans said the vote should occur on an amendment to energy efficiency legislation that is expected to reach the Senate floor in the next few days. That would present Obama with a more complicated choice, since large numbers of lawmakers in both parties are likely to favor the broader measure.
Sen. John Cornyn, R-Texas., said a vote on a free-standing bill that deals only with the pipeline is insufficient "because it will never see the light of day. The president's not going to sign it."
He said the pipeline's fate is in the hands of Senate Majority Leader Harry Reid, D-Nev., "and how serious he and our Democratic friends are about this issue."