The United States has been a long-time friend and ally of the Jewish state of Israel.
The vote was 62 to 37 but it did not reach the two-thirds threshold required to override.
The youth from South Dakota call the project a threat to their treaty rights and their way of life.
The Republican-controlled Congress doesn't have enough votes to override a veto.
The only two enrolled tribal members in Congress -- Rep. Tom Cole (R-Oklahoma) and Rep. Markwayne Mullin (R-Oklahoma) -- voted for the bill.
President Obama has said greenhouse gas emissions will be a factor in his decision on the permit for the project.
An amendment to require tribal consultation wasn't even put up for a vote.
Republicans tried to cut off debate and move the bill towards final passage.
Dozens of amendments have been filed so it looks like consideration might take a week or two.
Sen. Jon Tester (D-Montana), the ranking member on the Senate Indian Affairs Committee, joined Republicans in advancing debate on the measure.
Sen. Lisa Murkowski (R-Alaska) is moving forward even after Democrats forced the cancellation of a hearing on the bill.
Republicans are still planning to push for approval of the controversial pipeline.