I think Matt Yglesias is exactly right when he says the GOP's "Latino problem" extends far beyond immigration:
Consider the GOP's deeply racialized campaign against Supreme Court Justice Sonia Sotomayor. What was so surprising about this -- and I know I'm not the only fair-skinned English-dominant person with a Spanish surname who was genuinely shocked -- was that conservatives could have easily opposed her purely on policy grounds. Sotamayor is a fairly conventional Democrat on constitutional issues, and that would have been ample reason for conservatives to criticize her. Indeed, Justice Elena Kagan was attacked on precisely those grounds.But rather than tempering opposition with at least some recognition that Sotomayor's life story might be a great example for immigrant parents trying to raise children in difficult circumstances, the country was treated to a mass racial panic in which Anglo America was about to be stomped by the boot of Sotomayor's ethnic prejudice. The graduate of Princeton and Yale Law, former prosecutor, and longtime federal judge was somehow not just too liberal for conservatives' taste but a "lightweight" who'd been coasting her whole life on the enormous privilege of growing up poor in the South Bronx.
I would say this extends even beyond Sonia Sotomayor and also, say, campaigning on Sharia Law. When you have someone like Allen West out front saying something like this:
We already have a 5th column that is already infiltrating into our colleges, into our universities, into our high schools, into our religious aspect, our cultural aspect, our financial, our political systems in this country. And that enemy represents something called Islam and Islam is a totalitarian theocratic political ideology, it is not a religion. It has not been a religion since 622 AD, and we need to have individuals that stand up and say that.
And then you combine that with a presidential candidates signing a documents like this:
.... a child born into slavery in 1860 was more likely to be raised by his mother and father in a two-parent household than was an African-American baby born after the election of the USA's first African-American President.
And you alloy that to another presidential candidate saying something like this:
And so I'm prepared, if the NAACP invites me, I'll go to their convention and talk about why the African-American community should demand paychecks and not be satisfied with food stamps.
... what you start to get is the impression that you are looking at a party which represents the interest of those trying to keep you out. This impression is not wrong. Any serious conversation about Republican candidates needing to be more "diverse" needs to confront the hard reality of the Republican base.
Sheriff Arpaio does not owe his prominence to a military coup. He owes it to actual Republicans, virtually none of whom have any interest in seeing the party diversify on a policy level. Diversity isn't simply giving Mia Love a plum speaking spot. It is finding a Mia Love who represents the interests, and will advocate for policies, of other Mia Loves.
I don't think this is something you fix by 2016. This is a big problem. It took Democrats more than a half of a century of wandering to get it right.