Approval for the pipeline, which would transport oil from Canada's oil sands to the U.S. Gulf coast energy hub, has rested with the administration as it crosses an international border.
The decision has been pending amid jousting between proponents of the pipeline who say it would create thousands of construction jobs and environmentalists who say it would increase carbon emissions linked to climate change.
Passage of the companion bill was not assured in the Senate, which is expected to take up the measure next Tuesday. Supporters were still one vote shy of the 60 needed to overcome a filibuster, a blocking procedure, an aide to a Keystone supporter said on Friday, speaking on condition of anonymity.
Presiden Obama has said he does not want to interfere with the State Department review of the issue and that it was hard to evaluate the pipeline proposal until the actual route was known.
The White House has not made clear whether Obama would use his veto to block the legislation currently before Congress, but he has threatened to use that power in the past.
The congressional bills have highlighted both the importance of the pipeline to Louisiana, whose economy is heavily oil-dependent, and the fact that Obama cannot count on full support from members of his Democratic Party on some issues.
Democratic Senator Mary Landrieu, the head of her chamber's energy committee, is co-sponsoring the Keystone bill in the Senate with Republican John Hoeven of North Dakota. She is battling to retain her Senate seat in a runoff election against Cassidy on Dec. 6, after last week's midterm elections.