Former Massachusetts Gov. Mitt Romney holds a big lead over all other Republican primary contenders in New Hampshire, but businessman Herman Cain has surged into second place according to two newly released polls in advance of Tuesday’s Bloomberg/Washington Post Republican Presidential Debate in Hanover, N.H.

Congressman Ron Paul (R-Texas) climbs as high as the low double digits; all other candidates stand in single digits in both polls. Michele Bachmann, who charged from 4 percent to 12 percent from June to July, has boomeranged back to 3 percent or lower in the new polls.

Romney, the long-time frontrunner in the state, garners 37 and 38 percent support in polls by the University of New Hampshire and Harvard/St. Anselm released Friday and Monday, respectively. Cain earns 12 percent of Republican primary voters in the UNH survey —conducted in late September and early October — while he wins 20 percent in the Harvard poll conducted entirely in October.

The polls employ different sampling strategies — Harvard/St. Anselm matched phone numbers to voter lists, screened for past voting behavior and weighted the sample to exit poll demographics from the 2008 primary, while UNH called random phone numbers and interviewed respondents who said they would vote in the GOP primary, barring an emergency.

Voters sense Romney’s dominance in the state: fully 65 percent expect him to win the primary in the UNH survey. And a 52 percent majority of likely voters think he has the best chance of defeating Barack Obama in a general election. Nevertheless, more voters in both polls say their choice is dependent on which candidate matches their values or ideology rather than how competitive they will be with Obama in November 2012. And only a quarter of Romney’s supporters say they will definitely vote for him in the primary, opening the door for other candidates to chip away at his lead.

Former China ambassador Jon Huntsman earns 4 percent of the vote in Harvard/St. Anselm’s poll, but 8 percent in the UNH data. The latter represents a high water mark, up from 2 percent in July, but the poll’s favorable ratings indicate Huntsman — who has staked his candidacy on a solid performance in the state — faces an uphill battle going forward. At least as many voters have an unfavorable view of Huntsman (29 percent) as rate him favorably (27 percent), with a third of voters offering no opinion at all.

University of New Hampshire pollster Andrew Smith notes that much of Huntsman’s support comes from non-Republican voters who plan to vote in the GOP primary, rather than rank and file Republicans who make up the bulk of primary voters across the country.

Follow Post polling on Twitter

Like Post Politics on Facebook