Amid a debate within the Democratic Party about whether progressive ideas can sway voters in suburbia, candidates affiliated with an advocacy group that campaigns against gun violence sought — and won — elected office even in historically conservative suburban districts.

Moms Demand Action for Gun Sense in America appealed to suburban women on overhauling gun laws amid a rash of mass shootings in recent years, including the one in Parkland, Florida, in February.

The organization advocates so-called red-flag laws and banning bump stocks and assault weapons, and it opposes allowing guns on college campuses. It plans to achieve those policy aims by campaigning aggressively in future election cycles.

“Exit polling is still being parsed, but one thing is clear: In an election where women voters were crucial in swaying the balance of power, gun violence prevention was a priority issue for women from all walks of life,” the group’s founder, Shannon Watts, wrote about the midterm elections. “Gun violence isn’t a right-or-left issue — it’s a life-or-death issue.”

Putting that theory to practice, Moms Demand Action launched a formal training program last year for volunteers interested in running for office — an ambitious new stage for the six-year-old organization. It’s just one sign of the group’s growing influence: Everytown for Gun Safety, its parent organization, and Giffords PAC, another gun control group, outspent the National Rifle Association this midterm cycle.