Amnesty in its definition implies full pardon, forgiveness etc. and that's hardly what we want. If somebody says, hey you owe us 5-10k for X(whatever reason they can come up with really) over Y years that's hardly an amensty, since a) we would have to pay a fine b) register in some database and come out of the shadows as they like to put it.

Honestly, I am personally against a full amnesty simply because it will never get enough support. Hell, even if I was a USC, especially now, I would expect something out of this in terms of fines or whatever. In the eyes of the country i.e. average citizens, we aren't bringing much in except for workers and with the current state of unemployment that's hardly a positive impact. However if someone sugar coats this with something like "well, the immigrants will be required to pay substantial fines that will help us lower the national debt" we might actually get some support.