Republicans are split on the issue of illegal immigration.
To say that you are a conservative begs the question: Conserve what? The Republican Party is a place for various kinds of conservatives: religious conservatives, business conservatives, and cultural conservatives. Generally speaking, these groups overlap. The issue of illegal immigration highlights one area where they do not.
Business conservatives generally have no problem with immigration – legal or illegal. Some jobs can be exported and some cannot. For jobs like farming and construction, it makes sense to bring in lower-paid workers.
Cultural conservatives are threatened by immigration – legal or illegal. For them, the country is defined by a common language and culture. If you expect to live in this country, you should speak English and understand, if to subscribe to, Judeo-Christian beliefs and Western culture. To sacrifice this sense of nationalism for low-wages would be like encouraging your daughter to work as a prostitute. For cultural conservatives, values are more important than money.
Of late, national elections have been decided by one or two percent. Republican leaders realize that alienating even a fraction of any one of their conservative groups can cost them control. For them, the very fact that illegal immigration has become an important issue is to have lost on the issue. There is no obvious way to reconcile the views of these two very different kinds of conservatives.
For more on cultural conservatives, here's Jeralyn Merritt commenting on Tom Tancredo's stance on immigration as a threat to Western Civilization.
"Presidential candidate and U.S. Rep. Tom Tancredo told supporters gathered at a private ranch here Friday that American culture, as well as the fate of western civilization, is being threatened by illegal immigration.
....'There’s an issue that is so much broader than all that, so much more serious. It is the issue of our culture itself, and whether we will survive.'"