The advocacy groups have recast their cause as a public health and safety movement, and are homing in on areas where polling has shown voter support, like expanded background checks and keeping guns out of the hands of people with domestic violence convictions, restraining orders or mental illnesses.

Some of those provisions have gained steam even in heavily Republican-controlled state governments, like those in Louisiana and Wisconsin.

“Things that people feel are most doable politically right now are connected to domestic violence,” Mr. Webster said. “There is a lot of uptick on that issue even in red states and states with a lot of guns.” In the past two years, 11 states have passed such legislation.

Closing loopholes on background checks for gun owners is an area Americans support far more than steps like curbs on assault weapons or limits on magazine sizes. A recent Pew survey, for instance, showed that 52 percent of respondents said they believed it was more important to protect gun ownership rights. That figure was up from 29 percent in 2000. Still, in a 2013 poll, Pew found that nearly 75 percent of respondents supported background-check expansions.

Gun control advocates believe that ensuring background checks for the majority of gun buyers is the foundation of all other existing laws. “The reason voters support these laws is the same reason the movement supports these laws,” said Laura Cutilletta, a senior lawyer for the Law Center to Prevent Gun Violence. The same-sex marriage movement has been a model for advocates of new gun restrictions. As with gay marriage, background-check expansions enjoy far broader public support in polls than among elected officials, and they affect state residents immediately.

“The arc of the marriage-equality movement started in the federal government, and got them the Defense of Marriage Act,” said John Feinblatt, president of Everytown for Gun Safety, the gun control group backed by Michael R. Bloomberg, the former mayor of New York City. “Then they went to the states and showed that if you can get the majority of the public on your side state by state, that will influence the courts and Congress in the end.”

Their efforts have emboldened some governors and lawmakers, largely, but not exclusively, in solidly blue states. What is more, Gov. Dannel P. Malloy of Connecticut and Gov. John W. Hickenlooper of Colorado — both Democrats who pushed through a series of tough gun laws in their states after the Newtown massacre — won re-election. Two Colorado Democrats who strongly supported that state’s gun control package were booted from office in a special election in 2013. But the Democratic Party regained the seats in November.