Thoughts on immigration.

A friend of mine got married a few months ago to a lovely woman who happened to come from another country. She desired to retain the citizenship of her homeland; a practice that as far as I know is not uncommon. She was legally married here in the U.S. several months ago to her native U.S. husband. Only recently has she obtained a work permit of some type even though she has had a green card for some time now. Now, to be fair, I haven't meddled in the affairs of this friend, only hearing occasionally the frustrations of trying to get this piece of paper that would allow his wife to work in the U.S. It seems to me to be no wonder that people work here illegally. If it takes a woman who is legally married to a U.S. citizen 3 months or more to get the right documents to work, how could someone in more dire circumstances wait that long to work? Any bureaucracy that keeps this process backed up this badly, effectively only allows those privileged enough to not have to work to do so legally. Now, this could be an extraordinary case, however, I would venture a guess that it is not. So how do you fix this?