President Obama won the state by about 6 percentage points in 2012, and Shaheen retains the power of incumbency. However, her campaign funds are low for a senator seeking reelection: At the end of the year, she reported a little over $400,000 on hand.
However, Democrats pushed back on the poll, questioning the methodology and noting that it was conducted for a Republican firm.
"This is a partisan poll conducted by a group of Republicans who are all fresh off losing campaigns, and no one should take the data seriously," said Justin Barasky, spokesman for the Democratic Senatorial Campaign Committee.
The poll was released at a New Hampshire GOP organizational meeting held on Thursday night, at which Republican activists and elected officials met to make plans for the party going forward.
New Hampshire Republicans are reconfiguring after losing seats in the state Legislature as well as both congressional seats.
No Republican has yet emerged to challenge Shaheen, though former Rep. Frank Guinta, who was defeated in 2012 by Democratic Rep. Carol Shea-Porter, is considering the run. New Hampshire Republicans also believe former Sen. John Sununu and New Hampshire Senate Majority Leader Jeb Bradley could run.
RightOn Strategies, which commissioned the poll, is the firm of two former Guinta staffers, along with Mike Biundo, formerly national deputy coalition director for Mitt Romney.
The poll was conducted among 620 registered New Hampshire voters from Jan. 31 to Feb. 1 and has a margin of error of 4 percentage points.