You keep stating this as proof that we cannot do anything against illegals. Were this the case, the federal government could not deport illegals. So, quite frankly, you're full of it - those rulings you cite can only practically apply to LEGAL immigrants. If a court were to rule that illegals were eligible for welfare, in a sane, federalist society the moment they applied for welfare and were determined to be illegal aliens, the INS would be notified, they would be apprehended and then deported - so they can be eligible all they want, they just won't be around to collect. Instead, state and local governments get around this by simply looking the other way and ignoring federal immigration law - an area where the federal government has clear, CONSTITUTIONAL authority.
Are you getting the picture here? Although Congresscritter Tommy Temper Tantrum does not like it and although the boys in the pick up trucks don't like it, your federal government and mine and your state government, my state government and most other state governments simply do not choose to do what you want. This is nothing new. Most conservatives are all too used to their governments NOT doing what they want, law or no law.
If the "illegals" are here, those amendments also provide them with guarantees of various sorts which is why California has been ordered not to apply the result of the referendum which destroyed its Republican Party and, the other states understand implicitly that they will be treated likewise if they try to deprive the "illegals" of anything WITHOUT DUE PROCESS OF LAW.
Now, you might try to seek a federal court order in the nature of a mandamus (we command) ordering the federales to enforce their immigration laws and you MIGHT be successful but I doubt it.
One thing is for sure. A bunch of guys in pickup trucks (not Skinheads, not KKK, not whatever, just a bunch of good ol' boys, citizens, voters and veterans) are NOT going to force the government's hand.
What's more, plenty of people disagree with the idea that the government should knuckle under to you. Why do you suppose that all those governments are looking the other way? Is it because politicians are looking forward to getting themselves defeated?