How about two lines:
1. Like the current system, with limits etc., but, once you get in legally, you get benefits like public school, medical, etc. This can lead to citizenship.
2. Fast Lane, take all non-criminal comers, but you get no benefits and if you try to get them improperly, you get deported. This cannot lead to citizenship.
And, you cannot be in both lines.
In addition, everyone who is found to be present in the U.S. illegally gets deported and cannot get in line 1.
People will not stop breaking the law until there is are actual negative repercussions for doing it.
MotionMan
The US doesn't have the man power or the money to deport everyone.