Ugly numbers from the latest Daily Kos/Research 2000 poll:
The only problem is that the modern Republican party's panic switch, or at least one of them, is rancid jingoism and more or less open anti-Hispanic (though often specifically targeted at Mexicans) prejudice. Or, to put it more bluntly, as with African-Americans, it's tough to be the party of the blacks and the racists at the same time. (Not that the Dems didn't try it for a few decades in the middle of the 20th century — but it didn't end up panning out.)
One might imagine an alternative universe in which gays were not only an increasingly open and powerful political constituency but also one that was growing rapidly in population terms. And you'd have Republicans wanting to cultivate support among this growing group but also episodically bashing them to consolidate support among base conservative voters.
In other words, it's not a mistake or incompetence or any lack of planning that has Republicans in such a bad position with Hispanics, America's fastest growing ethnic group. It's just that people who are hostile to Hispanic immigration and just Hispanics in general are one of the GOP's key constituencies. That puts some real obstacles in the way of becoming the party of Hispanics.