The first state survey since the debate, taken by Magellan Strategies for the New Hampshire Journal, has the former Massachusetts governor leading with 42 percent, followed by Minnesota Congresswoman Bachmann and Texas Rep. Ron Paul at 10 percent apiece.
Former Alaska Gov. Sarah Palin and former New York Mayor Rudolph Giuliani, who have not announced, are next, followed by former Minnesota Gov. Tim Pawlenty.
Of respondents who watched the debate, 39 percent said Romney did best and 28 percent praised Bachmann.
Romney, Bachmann, Giuliani and Pawlenty have higher favorable than unfavorable ratings.
Former House Speaker Newt Gingrich and former Utah Gov. Jon Huntsman Jr., however, were disliked more than liked.
This survey of 727 likely Republican primary voters was conducted Tuesday and Wednesday with a margin of error of 3.6 percentage points.
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