When you add in those respondents who answered “all of the above,” more than three-quarters of Republican voters were deeply concerned about illegal immigrants abusing our health care system, schools and welfare programs. Among independent voters, a plurality of 43 percent listed it as immigration’s biggest consequence (which may explain why 72 percent of GOP voters and 54 percent of independents want legal immigrants to be admitted to the U.S. on the basis of merit or skills).

This is decidedly not how President Trump, conservative media pundits or GOP candidates talk about illegal immigration. By focusing on crime and job losses, the party and its leaders are making the least persuasive case for border security and immigration reform. As a result, Democrats feel little public pressure to compromise on the issue, even as their presidential candidates move aggressively leftward by promising the use of social services to illegal immigrants. If politics is a game of contrast, then the GOP can play it much better.

A similar lesson holds for cultural issues. When we drilled down, we found many examples where Republicans, independents and Democrats find common ground—and where the GOP can make major gains.