Oklahoma Gov. Mary Fallin, who chairs the National Governors Association and supports Keystone, said she asked Obama about the pipeline at a meeting with about 40 governors.
Obama yesterday told her he expects a decision "in the next couple of months," but didn't offer a specific timetable, Fallin and Nebraska Gov. Dave Heineman said.
Obama's comments were the most specific he has been in recent months about the 1,100-mile (1,900 kilometre) pipeline, which has become a high-profile symbol of the political debate over climate change.
Opponents say the pipeline would carry "dirty oil" that contributes to global warming, and they also worry about possible spills.
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Heineman, who supports the pipeline, said he was "pleased that we're finally going to get to a decision" on a project that has lingered for more than five years.
"This is very significant. It's been at least a year since I sent my approval to the president for our particular route (through Nebraska), and it's taken even longer than that on the federal level," Heineman said in an interview.
Review of the Canada-to-Texas pipeline remains at the State Department, Carney said.
Obama's comment comes less than a week after the project was thrown into apparent legal limbo, when a Nebraska judge overturned a state law that approved the pipeline route through that state.
Judge Stephanie Stacy ruled that Nebraska's five-member Public Service Commission should have decided the route.
Nebraska's attorney general has vowed to appeal the ruling, and the Calgary-based company that is building the crude oil pipeline called the ruling a "solvable problem."