Scott Brown is actually making use of the immigration issue in the New Hampshire Senate Race against Democratic Sen. Jeanne Shaheen,

Republican Senate hopeful Scott Brown is unleashing a new TV ad focused on border security against New Hampshire Democratic Sen. Jeanne Shaheen, tethering her to President Barack Obama on an issue that has dominated the headlines in recent weeks. The spot shows Brown, the former Massachusetts senator now running in the Granite State, talking to the camera, describing the various checkpoints Americans go through to get into government buildings, an airplane, a ballgame. “But folks who come here illegally, they just walk across the border,” he says, calling it “wrong,” as the camera pans over a field of low, dry grass. “Thanks to the pro-amnesty policies of President Obama and Sen. Shaheen, we have an immigration crisis on our hands,” Brown says. “We respond with compassion, but it’s time for us to secure the border once and for all.” [Scott Brown ad hits Jeanne Shaheen on ‘immigration crisis’, By Maggie Haberman Politico.Com, July 28, 2014 ]

Scott Brown is a moderate-ish Republican on many issues, otherwise he couldn't have had the success he had in Massachusetts.

But he has an obvious advantage over a Democrat on illegal immigration, and he may be able to take it farther—see Could Scott Brown Be A Pete Wilson-Style RINO Immigration Patriot Presidential Candidate? By Washington Watcher on January 18, 2014.