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Steven A. Camarota, research director at the Center for Immigration Studies, also disputed Mr. Aguilar’s conclusion that legalizing illegal Hispanic immigrants would be good for the GOP.

“The only way to come to the conclusion that accelerating immigration will help Republicans politically is to ignore all the survey data on what voters in immigrant communities want from government,” Mr. Camarota said. “Even with the current level of immigration, it is hard to see how the Republican Party survives as conservative and nationally competitive.”

But Texas GOP Chairman Steve Munisteri said Republicans should learn a lesson from post-election polls in Texas that showed Hispanics favored a guest-worker program — even if it does not include legalization of illegal immigrants.

Whatever the case, he said, the issue is so delicate that it could, over the long run, decide whether the Lone Star State stays in the Republican column.

“Currently, we get around 40 percent of the Hispanic vote,” he said. “If we have any major erosion among our Hispanic Republicans, if they get discouraged or disillusioned in any way, then Texas will be ripe for a Democratic turnover. So if you adopt a policy that turns off Hispanics in Texas that vote for the Texas Republican candidate, then the party will not survive nationally, and you cannot elect a Republican president in my lifetime.”