Hispanic voter growth, following population growth, has increased in both parties at similar rates (by 400% since '80 for Democrats and 350% for Republicans). That's bad for the GOP, which cannot hope to catch up with the Democrats by going slower than they are. Even if the growth rates were identical, the trend would bode terribly for Republicans. If we both double our holdings, but you held twice as much as I did before the doubling, the absolute difference between our holdings just doubled--in your favor!
The black vote as a percentage of both parties' total representation has remained pretty steady, at about an order of magnitude more substantial on the Democratic side.
Demographic changes have attenuated white dominance in the GOP as well, but the rate of reduction has been about half that of contracting white representation among Democratic voters. Democrats are (as a proportion of the total) losing whites faster than Republicans are, even though whites already favor Republicans. Keeping the country as Euro-descended as possible seems an obvious even though politically incorrect strategy for continued GOP competitiveness.
The other option is to go the McCain route. He spoke to three major Hispanic interest groups in July alone, and has thrown himself on the mercy of the NAACP, even as national polls show him carrying 1% to 2% of the black vote. He's refused to make an issue of Obama's racialist past, but has had no qualms decrying the 'biogtry' of restrictionists. The RNC evinced no concern about immigration at all.
From this vantage point, other than picking a VP to steal the spotlight from Obama, it seems as though he's doing everything possible to play to Obama's strengths and his own weaknesses (even admitting that he was until very recently a computer illiterate).
A few remarks on the tables above: All data are from the Presidential exit polls of their respective years with the exception of '06, which comes from a national sample of people voting in elections to the House of Representatives. The only adjustment I made was for the '04 Hispanic vote, 44% of which is shown to have gone for Bush in the national exit polling even though polling at the state level showed that to be an overstated absurdity (as John S Bolton identified and Steve Sailer refuted). I lowered Bush's Hispanic share from 44% to 40% and increased Kerry's from 53% to 57%.
The Asian and Other numbers are imprecise. In '88, whites, blacks, and Hispanics comprised 98% of the vote, so I assumed that Asians represented 1% of the total and that their votes went the same way as the national vote went. I did the same for Others as well. In '84, the Asian and Other vote combined for only 1% total, according to exit polls, so I split it evenly and again mirrored the national vote. In '80, exit polling data showed that 100% of the vote came from whites, blacks, and Hispanics. That wasn't actually the case, but their representations were too small to factor in. In '00, Asians jumped from 1% of the voting population as estimated by exit polling to 2%, and in '04 Others did the same, which is the reason for the relatively large increases for each between those respective years and the election cycle preceding them.