When Tom Tancredo entered the race for the White House, he never expected to win. Instead, he used the resulting exposure as a way to draw attention to the problem of illegal immigration. (That is why he brings up the issue in every one of his debate answers). However, I think that now he can rest assured that there is at least one Republican who will fight against illegal immigration.
Fred Thompson's immigration policy is exactly what conservatives have been pushing for months. In addition to the standard promises of no amnesty, a larger border patrol, and a border fence, Fred also supports harsh penalties for sanctuary cities (like Rudy Giuliani's New York) and verification that employees hired are legal residents. In addition, he also is in favor of ending the practice of giving legal status to relatives of people already here, something no other Republican supports. Tancredo can drop out of the race - there is now someone who will fight against illegal immigration.
(For the record, I checked Giuliani's and Romney's sites for their positions on immigration. Here is Romney's, and here is Rudy's.