Nate asks, "Can the Republicans win back the White House in 2012 or 2016 while losing further ground among Latinos?" I don't know about 2012 and 2016, but I can give my best estimates for 2008, based on my analysis with Yair using the Pew pre-election polls to get vote preferences (normalizing each state to line up with the actual election outcome) and the CPS post-election supplement to get voter turnout. (You'll get similar numbers using the exit polls, but I trust our analyses a little more, also they're consistent with our earlier graphs of voting by income and ethnicity.)
I'll show you what we found, then give some brief discussion.
Here's how Obama did among Hispanics in the states where there is a large Hispanic presence:
[In response to commenters, here are some numbers for McCain's estimated share of the two-party vote among Hispanics: NM 27%, CA 26%, TX 42%, FL 43%, AZ 35%, NV 24%, NY 25%, CO 27%, NJ 23%, IL 23%, CT 24%. Exit polls give slightly different answers. No data source is perfect and we have to acknowledge that there is uncertainty in our estimates.]
And here's a map showing our estimate of the Hispanic vote share by state (based on the CPS post-election supplement): Hispanics represented 31% of the vote in New Mexico, 22% in California, 20% in Texas, 15% in Florida, 13% in Arizona, 12% in Nevada, and less than 10% in all other states:
OK, so Obama dominated among Hispanics. How did he and McCain do among the rest of the voters? The following map shows our estimates from our model based on the Pew data:
This map looks suspiciously close to the map for all voters. And, in fact, it is.
Here's a scatterplot comparing McCain's vote share among non-Hispanics to his total vote share by state (excluding Alaska, Hawaii, and the District of Columbia):
The removal of the Hispanic vote wouldn't have changed the election outcome in any state (although New Mexico, Florida, Indiana, and North Carolina are within 1% of flipping, and small changes to the model (for example, using exit polls instead of the Pew surveys) might cause some of these to flip). The point is, except for the six or so states with lots of Hispanic voters, the changes are mostly tiny.
Now let's look at it another way. Instead of removing Hispanics from the equation (which helps the Republicans), let's try the counterfactual in which the Republicans give up on the Hispanic vote, which I'll operationalize by transferring half of McCain's Hispanic votes in every state to Obama. (For example, we estimate that McCain got 22.8% of the two-party vote among Hispanics in New Jersey. Under this counterfactual, we'll give him just 11.4%.) Here's what happens:
Again, not much difference. Ummm . . . Missouri moves to 50.3% for Obama. And here's the scatterplot:
The bottom line: Hispanics were not a key component in Obama's win. However, this is not to say that the Republicans should not try to contest the Hispanic vote. As the last scatterplot above shows, further losses of Hispanics would make the Democrats competitive in Georgia, Texas, and Arizona. In some sense this is no big deal, at least at the presidential level: If the Democrats remain at 53% or 54% of the vote, they'll win nationally in any case. If we imagine a national swing of 3% or so toward the Republicans, so they're competitive nationally, then their big risk if they lose Hispanic votes is to no longer be viable in Florida (where we estimate McCain to have won 43% of the two-party vote among Hispanics in 2008). That's the state where Republicans really can't afford to abandon the Hispanic vote.
P.S. Some commenters point out that the Hispanic vote is expected to vote. Following up on the above, I did some crude calculations, assumning that the Hispanic vote share increases by 20% in each state:
Again, the bottom line is that the biggest difference is in Florida, with its high Hispanic vote that is currently nearly evenly split between the two parties. Texas and Arizona show big potential shifts too, but, again, if these states are swinging without other big changes happening elsewhere, the national Republican party is in big trouble anyway.