A new poll suggests Scott Brown could win a Senate race in New Hampshire, for reasons that would be good news for Republicans in other states.

The survey of 827 randomly selected New Hampshire adults showed the former Massachusetts senator within two points of Sen. Jeanne Shaheen, the Democratic incumbent.

The WMUR Granite State Poll showed a 10-point improvement for Brown since January, who now scored 44 percent to Shaheen's 46 percent.

Should the poll hold up, it would mean the race has tightened much more quickly than either side expected. In most other recent polls, including one in June by WMUR, Shaheen has led Brown by low double-digits.

Republicans credit the shift, in part, to Shaheen's hyper-focus on New Hampshire issues in her campaign at the expense of hot-button national topics.

"Shaheen is running as Senator Pothole. She's trying to localize the race," said Ryan Williams, a Republican consultant who has advised Brown's campaign. "Scott's talking about big issues, like immigration, Obamacare and taxes."

Brown has been focusing in particular lately on immigration, and has in recent weeks run an ad in New Hampshire attacking Shaheen on the issue.

"Thanks to the pro-amnesty policies of President Obama and Sen. Shaheen, we have an immigration crisis on our hands," Brown says in the ad. "It's time to secure the border once and for all."

A memo by the National Republican Senatorial Committee this week pointed to immigration as a potential flashpoint in the race, noting "internal polls show that [Shaheen's] opposition to increased border security and her role in Obama’s push for 'Executive Amnesty' are extremely potent in the Granite State."

In a statement, Shaheen's campaign manager Mike Vlacich dismissed the poll, saying that their campaign has "been ready for a competitive race since day one."

"This race will come down to who makes a difference for people in New Hampshire, and Jeanne Shaheen's record is clear," Vlacich said.

If Brown is gaining ground because of national issues, it might be a trend that plays out in other battleground races.

The big question on the minds of Republicans and Democrats in Washington, however, is whether Brown's quick rise in New Hampshire is an anomaly or whether it portends better odds for Republicans across the country in November.

In past election cycles, New Hampshire has been uniquely susceptible to political waves, in part because the majority of its voters identify as independents. In 2008, when Shaheen won her seat, New Hampshire voters chose Democrats up and down the ballot. In 2010, the trend reversed.

Republicans are optimistic that this new poll might reflect a shift of public opinion in New Hampshire, and nationwide, in their favor. Democrats are also looking to New Hampshire for hints of what's to come, but they caution against reading too much into one survey.

"I think it's indicative of this poll and nothing else," said one Democratic strategist.