...cards to anyone who ask for them? Since the US constitution doesn't allow the Congress to pass laws restricting immigration, any law addressing that issue is unconstitutional, and therefore non valid.

If the laws really work, any foreigner has a right to a green card. He only has to be clever enough to travel to the USA and hire a lawyer, the rest is just the application of the Constitution. The immigration lawyers wouldn't tell anything about this because if they did they would loose their business, and your representatives wouldn't tell anything about this because if they did they would lose your votes ( and they also don't want to incorporate the currently Americans' prevalent xenophobia in the Constitution ).

Anybody with a green card can be a US citizen in 5 laws, with no exception.

(correction in the last sentence: not 5 laws, 5 years)
@Escher: no judge would buy that argument. If are really interested in the Constitution, I recommend you this page: http://federalistblog.us/2006/07/delegated_powers_immigration.html