This might be a good time for me to re-post this essay I wrote a couple of years ago: Here’s a video version (from a Federalist Society panel discussion, at about 4:50 through 19:10).
The most important are the first and last: not focusing enough on assimilation and not striking a pro-immigrant tone. Correcting the former (and it ought to be kept in mind as immigration legislation is drafted) should reassure a lot of folks on the right, and correcting the latter should help a lot with voters in high-immigrant groups. The worst thing would be to try to buy votes by supporting programs that give special treatment to, say, Latinos and Asians: That would be divisive, not to say unconstitutional, and Republicans will never be able to out-promise the Democrats here. Nor should they want to: E pluribus unum.