After the defeat of Mitt Romney on November 7, alongside several Republican Senate candidates vying for seats they were once favored to win, Republicans began wringing their hands over the future of the party. The election showed that the GOP was losing the demographic battle. A party of rural whites was clearly in trouble unless it found a way to broaden its attractiveness to Latinos, who voted for Barack Obama two-to-one, and other growing ethnic groups. “Unless we do that we’re going to be a minority party,” warned Newt Gingrich.

Skeptics have wondered if the GOP was really capable of change. Newtown offers Republicans their first test.

Much of the post-election discussion focused on immigration, an issue of obvious import to Latinos. Yet Latinos are hardly single-issue voters who care only about immigration reform. Appealing to this constituency is going to require the GOP to do more than provide undocumented immigrants a pathway to citizenship. Republicans must show they support a variety of issues important to the Latino community.

Gun control is one of those issues.

Polls show that Latino support for gun control is greater than that of any other major ethnic or racial group, including African-Americans. A Pew Center study in April of this year found that when whites were asked which is more important, protecting the right of Americans to own guns or controlling gun ownership, 57 percent sided with the right to bear arms. Latinos, by contrast, were much more favorable to gun control. Only 29 percent of Latinos said protecting the right to bear arms was more important.

Other polls show that 69 percent of Latino voters believe the laws governing the sale of firearms should be stricter. Only 24 percent say they should remain the same. Unlike many gun-rights activists, only 5 percent of Latino voters say America’s gun laws should be less strict.

Latino support for the types of reform being talked about in the wake of the Newtown massacre is particularly strong. Take, for instance, mandating universal background checks for all gun purchasers. Under current law, only sales conducted by licensed dealers must involve a background check to see if the intended purchaser has a criminal record or a history of mental illness. Because you don’t need to have a license to sell a gun, it’s estimated that 40 percent of lawful gun sales are completed without a background check.

Latinos overwhelming support closing down this “private sale” loophole. A recent poll found that 86 percent agree that every gun sale should involve a background check.

Over the past year, Republicans in Congress have been pushing for a new federal gun law—one that would expand, rather than restrict, gun rights. The proposal, called National Right to Carry Reciprocity, would allow people with permits to carry loaded guns in states with loose rules, like Utah, to bring and carry their guns in any other state, even states like New York that restrict public possession of firearms. Although strongly favored by the National Rifle Association, the proposal is just as strongly opposed by Latinos. Indeed, even 70 percent of Latinos who self-identify as Republicans oppose this law.

Can Republicans break from their longstanding allegiance to the gun lobby and find a way to support modest gun-control laws like universal background checks? It may be that the future of the GOP depends on it. The demographic shifts America’s undergoing, including the growing number of Latinos, demand it.