CONCORD, N.H. — New Hampshire’s late state primary leaves relatively little time for the winners to pivot toward the general election, so some candidates and parties are already thinking about November.

Republican U.S. Senate hopeful Scott Brown has run frequent ads targeting incumbent Jeanne Shaheen while barely mentioning his opponents in the Sept. 9 primary: former U.S. Sen. Bob Smith and former state Sen. Jim Rubens. The Democratic Party has been focusing much of its firepower on Brown and Walt Havenstein, one of the Republicans hoping to face Gov. Maggie Hassan, while paying little heed to Smith, Rubens or Havenstein’s opponent, Andrew Hemingway.

“Certainly Scott Brown has been running what looks like a general election campaign from day one,” said Dante Scala, a political scientist at the University of New Hampshire. “He certainly has visited local Republican groups, and courted Republicans and done all of that. But his message has been very much a general election message.”

Scala said the approach is the right one for Brown.

“That strategy makes perfect sense,” he said. “When you have the name ID that Scott Brown had when he entered the race and you’re facing two rivals who are much lesser known, there’s no reason to discuss them or attack them. The best thing to do is just starve them of oxygen.”

It’s not to say Brown isn’t campaigning. He keeps a full schedule and has traveled all over the state since formally entering the race in April, doing the kind of door-to-door politicking and town-hall-style meetings that New Hampshire voters have come to expect.

“Scott Brown is taking nothing for granted and is working hard for every vote in the primary election,” said Elizabeth Guyton, the Brown campaign’s communications director. “He’s participating in five debates with his GOP primary opponents, and is running a traditional New Hampshire-style grassroots campaign.”

The state Democratic Party also appears to have leapfrogged the Senate and gubernatorial primaries, putting the bull’s-eye squarely on Brown and Havenstein while giving scant recognition to the other candidates. For example, in scores of party press releases going back to mid-July, Brown and Havenstein are in headlines repeatedly, Smith and Rubens and not mentioned at all and Hemingway gets one mention.

“I think the state Democrats have essentially been making bets, wagering that Brown will be the nominee and therefore going after Rubens or Smith is a waste of time and money and resources,” Scala said. “With Havenstein, I think they’re working under the same assumption.”

Julie McClain, a spokeswoman for the Democratic Party, said Brown’s fundraising, name recognition and backing from big name Republicans like Mitt Romney, John McCain and the state’s other senator, Kelly Ayotte, make him the candidate to beat.

“If he doesn’t win this primary with 80-90 percent of the vote it should rightfully be seen as a disappointment,” McClain said.

Attacking Havenstein is sort of a no-lose proposition, Scala said: The party started to define him early and can keep the drums beating through November; or, if they hurt him badly enough before the primary, maybe Hemingway wins and Hassan faces an underfunded candidate in November.

For most of the Republicans involved in the primary, it’s less risky to go after the Democrat. Hassan is the only Democrat at the top of the ticket to face a primary and is expected to easily top her two rivals.

“Going negative is very tricky in primaries because while Republicans are all for beating up Democrats, Republican voters are much more ambivalent about Republicans going after other Republicans,” Scala said. “It’s a fight within the family all of a sudden.”

Hemingway, with relatively little name recognition and a huge financial disadvantage, is an exception.

“He can’t afford to just sit there and be a nice Republican,” Scala said. “He has to find a way to engage Havenstein. He has to take that risk because there’s no other road to victory.”

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