The bipartisan 63-32 vote was 3 more than the 60 required, and well above the highest level the highly controversial measure gained in recent years when Democrats controlled the Senate. With more than enough votes at their command, Republican and Democratic supporters said they hoped the legislation could win final approval and be sent to the White House by the end of next week.

“President Obama has every reason to sign the jobs and infrastructure bill that we will pass,” said Senate Majority Leader Mitch McConnell of Kentucky. He noted that the Nebraska Supreme Court had recently rejected a legal challenge brought by opponents, an obstacle the White House had cited.

Sen. Brian Schatz, D-Hawaii, made the case for the opposition. He said that if constructed, the pipeline will carry “some of the dirtiest, most dangerous and most polluting oil in the world.”

The proposed 1,179-mile pipeline would begin in Canada, enter the United States at Morgan, Mont., cut across South Dakota and connect with an existing pipeline in Steele City, Neb. that in turn reaches refineries along the Texas Gulf Coast. It would carry an estimated 800,000 barrels of crude oil a day.

The White House has repeatedly threatened a veto. If Obama follows through, it will become the first of what are expected to be numerous clashes with the Republican majorities now in control of both houses of Congress.

Since Congress convened on Jan. 5, the White House has issued a total of five veto threats, including two Monday.

The Republican-controlled House passed pipeline legislation last week, as it often has in recent years. This time, for the first time since the project was proposed six years ago, the Senate is in Republican hands and the legislation commands enough bipartisan support to assure its approval — if not enough to override a veto.

The most recent Senate vote, held in December, was on passage of a bill identical to the one voted on Monday. That gained 59 votes, one shy of the number necessary to advance to a floor vote.

This time, 52 Republicans, 10 Democrats and one independent voted in favor. All the votes in opposition were cast by Democrats.

By bringing the legislation to a vote one week after taking over the Senate majority, Republicans hope to achieve two goals at once: Passing the measure and ushering in a new era of open Senate debate with the opportunity for lawmakers to seek votes on proposed changes.

“It’s the latest example of Congress getting back to work under a new Republican majority,” said McConnell, in a jab at Democrats who have generally blocked votes on amendments over the past few years.

Democrats said they welcomed that, and some readied proposed changes designed to put Republicans on record concerning climate change.

The pipeline project has unanimous support from Republicans in Congress, but it divides Democrats. Environmentalists generally oppose the legislation, while several unions support it for the jobs it would create. There was significant debate Monday over both the proposed project’s impact on the environment and on the economy.