I dont think that the whole "we are all immigrants to the USA" argument holds anything at all at this point. Sure, everyone migrated to this land and established a country.. but now it is a fully running, independent country which is filled mostly with people whole were born here in America... thus making us Americans, not "people who came from people who migrated to here."
I agree with just about everything MetalKingdom has said. We have an established WORKING system, and for someone to come and ignore that system, will be throwing a wrench into a gear. If someone enters our country un documented, and goes on a murder spree, what are the chances of anyone ever finding the guy? He's faceless, nameless, and completely unknown to the US.
Sure that example is a little extreme, but it could happen.
And yes, most of them dont give a shit about this place, the protestors who were marching around with the American flag were only doing it to try to get us citizens to side with them because they know we're all so "patriotic" and love our country... so if they hope that by showing some love for the US that all of the flag waving citizens will think "well they are proud US citizens and love America, lets treat them like Americans!" But in reality, they probably dont give a shit about the US, just like none of us really give a shit about Mexico.
When it comes down to it, I think that if any of them want to be US citizens.. then they should become US citizens… nothing is stopping them, just do it legitimately, become a real US citizen, learn the language.. then you can get a job doing something other than picking strawberries for 20 dollars a day.