The basic problem is that Thompson's policies are nowhere near the level of enforcement you need to handle a situation where the profits from illegal immigration are huge for employers. Thompson's policies would barely dent the lowering of US wages and job quality associated with recent immigration policies (and might not even do that if legal immigration were expanded enough). Thompson also doesn't handle the potential for increased US immigration enforcement to destabilize Mexico—which has become rather dependent on remittances.
I'm glad to see that Thompson is at least paying attention to the immigration issue—but a lot more work is needed before there will be something on the table the bulk of Americans would recognize as a solution.