More generally, we can say that non-whites overwhelmingly vote Democrat, insofar as they vote. Of voting non-whites in the U.S., around 70% vote Democrat. Whites currently constitute no more than 70% of the U.S. population, and will be a minority before the end of century--likely before then.
One wonders why Asians and Latinos vote Democrat. Is it an image-based phenomena--certainly, members of the Democratic Party are on average more oriented toward multiculturalism and acceptance of "others." (But at the same time, Asian and Latino populations are often coming from very socially-conservative backgrounds, which might make the GOP image seem more appealing.) Also, the GOP has a reputation for supporting controls on immigration.
Or is the voting phenomenon under discussion more issue-based? Latinos earn, on average, less than their non-Latino white counterparts. Perhaps they have a greater interest in progressive taxation, and more interest for government services such as healthcare and public education. With certain Asian groups, there is a similar situation.
There is also the issue of Affirmative Action. This benefits, at least on a surface level, both Asians and Latinos. The GOP--although not John McCain--has been more strongly opposed to Affirmative Action than the Democrats. (One hopes that Affirmative Action is not the draw for Asians and Latinos, as this suggests a rather crass racialist politics, and also because the future of these programs, and thus the potential draw to the DP, is rather in question.)
Finally, there is foreign policy. I wouldn't wish to cast aspersions upon the loyalties of Asian-Americans, but one must wonder whether they might oppose military build-ups that would threaten their home country, e.g. China. More generally, there is less of a connection to the American military machine among immigrants, relative to the native-born, and that also influences perceptions of what America does with its often rather hard to follow military deployments.
Whatever draws Asians and Latinos to the Party, more must be done to get them registered and voting. This is particularly true when it comes to Latinos. (One might note that such activity may even benefit the GOP in acting to convince them that Latinos really do exist as members of the Republic and that current trend point to white minority status at the political level as much as in other areas.) George W. Bush might not have won the last election if Latinos had been sufficiently mobilized. I fear that the coming election too will be lost to the GOP because of lack of voting among the non-white community, part of which is still stuck in permanent resident status rather than acting as part of the citizenry.
One solution, looking to 2012, would be to grant illegal immigrants amnesty and quick access to citizenship in return for a reduction in the amount of legal immigration, thus shifting us down the process toward white minority status without actually speeding up the process over the long run.
On the other hand, one must recognize that movement toward minority status will make many whites vote GOP, esp. if that party ever supports immigration policies substantially different from those of the DP. However, this conversion process from DP to RP will likely take quite a bit of time, and so shouldn't be a huge problem, from the DP standpoint, for 2012, even if amnesty is enacted.
Looking to the long-term, a major goal, besides getting more Latinos as citizens who are registered and voting, must be keeping white in the Party and, indeed, evening expanding white participation, particularly among males. With Bill Clinton and the changes he made to the DP, it seems we are already moving in that direction. However, once the GOP no longer has the war issues alternately hurting and helping it, the field will be quite different. If the GOP can really act as the party of smaller government, that will attract many white voters, and may also make strong inroads among the Asian-American community. (You might say, though, that hell is likely to freeze over before such happens.) What would the Democratic Party offer then, once its anti-militarism cards were gone?
One issue might be "progressive taxation." Historically this term has been disturbing for many. Obviously, one must not go overboard with such. But it is at least possible to target tax-cuts, as economic growth increases revenues, toward the lower tax-brackets. For example, one might do away with the farce of claiming that Social Security taxes have some fixed connection to Social Security expenditures, and lower these taxes while maintaing the same level of benefits.
Ideally, the Republican Party will call for cuts in Social Security through severe means-testing (with exceptions made out of fairness to the very old--e.g., in 2020, those born before 1940). Then it might be time to abandon the Democrat Party. In the mean time, one hopes that the DP might push for more progressive funding of the same benefit levels to which both parties are committed.