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Mr. Fineman, whose organization called for a boycott of the Starbucks chain because of its policy of allowing gun owners to carry firearms legally in its shops, said Congress won’t address gun control unless the public exerts economic pressure in their states. Those and other boycott threats pressured the coffee-shop chain to publicly request that gun owners not bring weapons into the stores.

“We would target a couple of these states — Wyoming for example, where both senators voted against the background check law,” Mr. Fineman said. “We would simply let those senators know that if they didn’t vote for the law, we would call for a boycott of their state. If you don’t vote for it, we’re going to hurt your state, big time. This country runs on money. It’s as simple as that.”

Mr. Gross of the Brady Campaign said his group still sees opportunities for persuasion in the Senate, mentioning specifically Sen. Kelly Ayotte, New Hampshire Republican who voted against the background check measure in April.

“You have to look at this in the context of what it takes to pass a sensible gun law,” Mr. Gross said. “The Brady Law took six votes over seven years to pass.”

He said it was a positive sign for gun control advocates that six senators who had received an “A” rating from the National Rifle Association voted for expanded background checks last spring.

“That’s genuine progress,” Mr. Gross said. “That progress came about, we believe, because of the leadership of the White House but more importantly because of a new level of engagement among the American public. It may not be tomorrow, it may not be within the next year, but we are on a trajectory that gives us hope and inspiration that we will get there.”