The WMUR Granite State Poll shows Obama leading Romney 52 to 37 percent among likely voters. Nine percent said they are still undecided.
The poll of 600 likely general election voters was conducted by landline and cellphone from Sept. 27 through Sept. 30 for WMUR by the University of New Hampshire Survey Center. It has a margin of sampling error of plus or minus 4 percentage points.
UNH pollster Andy Smith said there has been a significant shift in which party is energized.
"Right now, the voters most interested in the election are Democrats," Smith said. "That is a good sign for the president because you really have to get energized, angry, motivated voters to get to the polls, and right now, that's the Democratic Party."
The poll also shows that Obama is winning over independents. After being neck and neck last month, the president now leads that group by 16 points.
Obama has also has seen a boost in his favorability rating. The polls shows that 56 percent of those surveyed have a favorable opinion of the president, while 40 percent do not.
"If you go back to August, it was a tie at 48 percent favorable and 48 percent unfavorable," Smith said. "He has really done a good job of buttressing his image here in the state."
Romney's favorability numbers are going the wrong way in the most recent poll, with 39 percent having a favorable opinion compared to 54 percent with an unfavorable opinion.
Smith said a good showing in the Wednesday's debate could help Romney, who might also benefit from new ads.
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