WASHINGTON — The families of the Newtown, Conn., shooting victims who have converged on Capitol Hill this week made a point of visiting Senator Heidi Heitkamp, a freshman Democrat known for the “North Dakota nice” of her home state, but on the main issue that brought them here — limiting the capacity of gun magazines and universal background checks — she curtly rejected their pleas for support.

“In our part of the country, this isn’t an issue,” Ms. Heitkamp explained in an interview afterward. “This is a way of life. This is how people feel, and it is extraordinarily difficult to explain that, especially to grieving parents.”

Bottom line, she said, “I’m going to represent my state.”

For years, guns have been the issue that swing-state Democrats like Ms. Heitkamp have sought to bury. Leading Democratic strategists still believe the assault weapons ban and the creation of background checks were a driving force in the Republican landslide of 1994. Six years later — after the Democratic presidential nominee Al Gore lost his home state, Tennessee; once-reliably Democratic West Virginia; and Arkansas, home to Bill Clinton, amid an onslaught of advertising by the National Rifle Association — many of those strategists vowed to let the issue of gun control lie dormant indefinitely.

But many Democrats insist the mass shootings in December at Newtown, after similar shootings in Aurora, Colo., Tucson and Virginia, have changed the politics of guns.