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The Senate has failed to move forward on the Keystone XL Pipeline Monday evening, extending the battle over the controversial Canadian oil import project that is one of the Republican Party's top priorities since taking over control of the Senate in January.

The Senate voted 53 - 39, falling short of the 60 vote requirement to pass the critical procedural hurdle.

When the Senate passed a similar procedural motion related to the Keystone bill on January 12th, which also needed 60 votes, 11 Democrats joined 52 Republicans to pass the motion. But fewer Democrats supported the vote this time. Instead they protested the way Senate Majority Leader Mitch McConnell is running the floor and the amendment process.

“Senator McConnell promised Democrats an open amendment process and a full throated debate on the Keystone pipeline, and we are holding him to that promise," Sen. Chuck Schumer, D-New York, said in a statement. "Trying to muzzle the debate by refusing to allow Democrats even one minute to advocate for their amendment and then simply refusing to hold votes on dozens of other amendments is not a remotely ‘open’ process."

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McConnell complained on the Senate floor, saying he heard Democratic leadership was "pressuring" its members to vote against the motion.

"We've heard rumors that some in the Democratic leadership are pressuring rank-and-file Democrats - even Democrats who cosponsored this bill - to block Keystone's jobs with a filibuster instead," McConnell said on the floor. "This is really disappointing when you consider all that our friends on the other side have been saying about the filibuster for so many years."

But some moderate Democrats who support the pipeline said they just wanted to move on."I think we should move on right now, take this to a final vote, and move on," Sen Heidi Heitkamp, D-North Dakota, who was one of four Democrats to vote for the measure, told reporters after the vote, "Now, would this vote have been different had the process been different on Thursday? Yea."

McConnell could bring the vote to the floor later this week.

President Barack Obama has threatened to veto the stalled project that he says could have a harmful impact on the environment and will do little to help the American economy.

Republicans made the pipeline their top priority at the start of the new Congress and are anxious to force the president's hand on what Senate Majority Leader Mitch McConnell calls a "jobs and infrastructure bill."

A number of senators did not vote, including critical Republicans who were needed to advance the bill.

Leading senators did not vote that would have helped Republicans get closer to 60, including Sen Marco Rubio, R-FLorida, who is out of town this week fundraising for his potential presidential race, his office confirms. And Sen John McCain, R-Arizona, is on his way to Saudi Arabia for the funeral of King Abdullah.

A two-thirds majority in both chambers of Congress is necessary to override a presidential veto.