Despite a recent surge in the polls, Sen. Bernie Sanders, I-Vermont, pledged once again that he'll support the eventual Democratic nominee and forego an independent presidential bid if he isn't the nominee.

The new CBS News Battleground Tracker poll shows Sanders leading Democratic candidate Hillary Clinton in both Iowa and New Hampshire. His lead is 10 points among likely Iowa Democratic caucus-goers and 22 points among likely New Hampshire Democratic primary voters. In South Carolina, Clinton still leads Sanders by 23 points.

Although he's officially an independent senator, Sanders decided to compete for the Democratic nomination. He's said since he announced his candidacy that he would not run as an independent, and he said Monday that "of course" he still plans to hold to that pledge despite his recent success.

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Sanders said he thought about running as independent in the first place, but decided not to.

"If we were serious about winning this election, which is always my intention from day one, I thought we could and I hope that we will. I had to do it within the Democratic primary caucus process," he said.

"What I did not want to do is run as a third party candidate, take votes away from the Democratic candidate and help elect some right-wing Republican. I did not want responsibility for that. So what I said at the beginning of the campaign is that I was not going to run as an independent. And I say it now, that if I do not win this process I will not run as an independent."