The vote in the Republican-controlled House comes in the wake of the Supreme Court's ruling that most of the law is constitutional. In response, Republicans vowed to continue efforts to undo the law, and the House late Thursday released the Repeal Obamacare Act to do just that. 

Democrats hailed the high court ruling and lauded Chief Justice John Roberts for joining the four more liberal justices on the Supreme Court in upholding the mandate to have insurance. Justice Anthony Kennedy, who was thought to be the most likely of the other five justices to uphold the law, joined the three other justices in ruling against the healthcare reform legislation. Reid said he was "very pleased" with Roberts's opinion on the case.

"I think that that speaks very highly of how important that case is and how important it was that he be on the winning side. So I was very happy," Reid said.

Reid said he was surprised with the ruling, and especially with how Roberts and Kennedy came down.

"I thought that Kennedy was the person that would be the swing vote and I thought that it could be a 6-3 decision," Reid said. "But it wound up being 5-4 with Kennedy going way off the reservation, which he has quite a bit lately. I've been fairly disappointed with him."

The majority leader added that he would call Roberts because he was "very proud of what he did."

In the same interview, Reid also said in the next Congress he would move to reform the filibuster.

"It's long overdue. The filibuster was originally set up to help legislation get passed, it's not part of the Constitution, it's just something we did to move legislation," Reid said.

Reid would not go into detail about what parts about the filibuster he wanted to reform in particular, but he said one change would be to get rid of the motion to proceed to a bill.

"For me to get on a bill, this past year and a half, has taken me 10 days or two weeks. That should not be the case. We should not have to have a motion to proceed," Reid said. "It's a debilatory tactic and we need to get rid of it."