WASHINGTON — President Obama is finding himself increasingly boxed in on the Keystone pipeline fight as more Congressional Democrats are joining Republicans in backing the project, which has strong labor support and could generate significant numbers of jobs in economically hard-hit states.

On Wednesday, the House passed a short-term transportation bill that included a provision that would pave the way for the construction of the next stage of the oil pipeline, a measure that Mr. Obama has said he would veto. The bill passed 293 to 127, with 69 Democrats supporting it.

It is the fourth time the House has passed a measure to expedite the project; one failed narrowly in the Senate only after Mr. Obama personally lobbied some Democrats to vote no. With the House vote, Mr. Obama finds himself, for the first time in his presidency, threatening a veto on a significant piece of legislation that enjoys the support of an increasing number of Democrats, as well as the vast majority of Republicans in Congress.

With gas prices sticking near $4 a gallon, unemployment high in many states and demonstrable support for the project in numerous polls, many Democrats — especially those from states where pipelines are commonplace — are beginning to sound almost indistinguishable from Speaker John A. Boehner, who called Mr. Obama “increasingly isolated” in his opposition to expanding the project.