As if President Bush understands what most people want less well than you...aren't you the real MENSA type?!
You've really got two options, I'll tell you what they are but you probably aren't ideologically capable of accepting either. After I tell you the *only* two options available you'll no doubt plead for a 3rd option of "enforcing existing laws" (yeah, that's worked really well so far).
Option 1. Leave all illegals unregistered and anonymous.
Option 2: Offer enough of an incentive to convince illegals to voluntarily register themselves with the federal government.
Oh, by the way, if the gun banners ever seize power because of the efforts by people like you to knock down our pro-gun politicians with friendly fire, those gun banners will *first* find ways to register all gun owners.
It's easier to ban things and people after they have registered than when they are anonymous, after all...something that the gun banners understand far better than the immigration dilettantes.