Manchester, New Hampshire (CNN) - A second state poll indicates that Mitt Romney's still ahead of the rest of the field of Republican presidential candidates in the first-in-the-nation primary state of New Hampshire, but that Hermain Cain's numbers are on the rise.
According to a new survey by Institute of Politics at Harvard University and the New Hampshire Institute of Politics at Saint Anselm College, 38% of likely Republican primary voters say they would definitely or probably vote for Romney, the former governor of neighboring Massachusetts who's making his second bid for the White House. Romney has been the front-runner in just about every GOP primary poll in the Granite State over the past year.
In the poll released Monday, one day before a Republican presidential debate at Dartmouth, New Hampshire, Cain, the former Godfather's Pizza CEO and radio talk show host, is at 20%, with Rep. Ron Paul of Texas at 13%.
A WMUR Granite State Poll conducted by the University of New Hampshire that was released Friday had Romney at 37%, Cain at 12%, up ten points from July, and Paul, who's making his third run for the presidency, at 9%.
According to the Institute of Politics at Harvard University and the New Hampshire Institute of Politics at Saint Anselm College survey, 5% of likely Granite State GOP primary voters say they will definitely or probably support former House Speaker Newt Gingrich, with former Utah Gov. and U.S. ambassador to China Jon Huntsman and Texas Gov. Rick Perry both at 4%, and Rep. Michele Bachmann of Minnesota at 3%. Former Sen. Rick Santorum of Pennsylvania and former New Mexico Gov. Gary Johnson are both at 1%, with 11% undecided.
"Polling at only 4%, Rick Perry is in a statistical dead heat with former Governors Gary Johnson and Jon Huntsman - and not Mitt Romney. Clearly, this is not the position that he envisioned for himself when he entered this race," says John Della Volpe, director of polling at the Institute of Politics at Harvard University.
"While Governor Perry trails Mitt Romney by more than 30 points - this race is far from over. There's opportunity for a strong Romney challenger to emerge - while Romney is the choice of 38% of likely Republican voters - only 10% say they are 'definitely' voting for him," adds Della Volpe.
The poll indicates that only 6% say they're definitely voting for Cain, who has surged in national polling the past two weeks.
According to the survey, only 14% say they are 'very satisfied' with the field of GOP presidential candidates. But 72% say they think Romney would win a 2012 general election matchup against President Barack Obama, with one in five saying the president would win re-election.
Romney has made a few appearances this year in Iowa, the state that kicks off the presidential caucus and primary season, but he has spent much more time in New Hampshire, the state that goes second in the race for the White House.
Huntsman appears to be betting all his chips on a strong showing in the Granite State, which comes second after Iowa in the primary and caucus calendar. Bachmann is spending much of her time in Iowa.
The poll also indicates that slightly less than half (46%) of likely Republican primary voters say they support the tea party movement. Of those voters, 30% say they support Cain, with 29% saying they back Romney.
The Institute of Politics at Harvard University and the New Hampshire Institute of Politics at Saint Anselm College poll was conducted Oct. 2-6, with 648 likely GOP primary voters in New Hampshire questioned by telephone. The survey's overall sampling error is plus or minus 4.4% pts.
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