Two points: First, the divide on immigration is not between conservatives and liberals, it’s between the elite and the public, with the public (of whatever party) generally supportive of strong controls and lower levels and the elite (of whatever party) generally hostile. These kinds of gaps exist in other areas as well (like abortion), but the gap on immigration seeems to be wider than on other issues, reflecting Huntington’s point about a nationalist public and a cosmopolitan, post-national elite.
Second, to state the obvious, the importance of issues to voters fluctuates, and elections are likely to hinge only on issues that are among the top two or three for large numbers of voters. Immigration was a politically salient issue 10 years or so ago (Pete Wilson won reelection in 1994 only because he hitched his wagon to the anti-illegal-immigration Proposition 187), then ebbed, and since 9/11 has been gathering steam politically — i.e., has been getting more important to more people. A Rasmussen poll from last month found that fully 29 percent of respondents said immigration was a more important voting issue than Iraq (54 percent said Iraq was more important), which seems pretty high to me, given the importance of the war.
A good roundup of polls on immigration is here.