The survey, from New England College, gives Sen. Jeanne ShaheenCynthia (Jeanne) Jeanne ShaheenWeek ahead: Crunch time for defense bill’s cyber reforms | Equifax under scrutiny Five things to know about the Kaspersky-Russia controversy DHS bans Kaspersky software in federal agencies MORE 51 percent of the vote to the 32 percent that support her potential Republican opponent, former Rep. Charlie Bass. Bass hasn't yet entered the race.

She remains popular in New Hampshire, with 56 percent of respondents approving of her job performance, while a third disapprove.

Republicans had long hoped they could take on Shaheen in 2014, but she hasn't yet met a credible challenger, and her favorables remain high.

And the main line of attack they've begun to build, based on opposition to the Affordable Care Act, looks to fall flat in New Hampshire. This new survey shows 58 percent of respondents supporting the law.

In New Hampshire's two congressional districts, Rep. Annie Kuster (D) fares better than Shea-Porter, as expected for the two incumbents.

Kuster takes 46 percent support to former state Sen. Gary Lambert's (R) 26 percent support, while another 28 percent are undecided, an unsurprising outcome in the more Democratic of New Hampshire's two congressional districts.

Shea-Porter, however, is in a statistical tie with Guinta, who announced last month his plans to pursue his old seat. She takes 43 percent support to his 42 percent support, with 15 percent undecided, and her approval rating is only at +3 percent.

Both incumbents are GOP targets, but Republicans feel they have a better shot at Shea-Porter, who represents a swing district that narrowly went for President Obama in 2012.

President Obama is, however, well-liked, with 55 percent of respondents approving of his job performance and 42 percent disapproving.

The survey was conducted among 1,063 registered voters from Oct. 7-9 and has a margin of error of 3 percent overall, 4.12 percent in the 2nd District and 3.29 in the 1st.