It comes back to the question of being an illegal alien really. Once found deportable, or arrested for something and subsequently found guilty, deportation is the way to handle that in most cases. A criminal, especially one that committed their crime(s) in the US, has no right to asylum whatsoever as far as I'm concerned.
If they are going to be mistreated in their country of origin, too bad for them. They shouldn't have illegally come to the US and then mistreated our citizens by committing crimes.
There is no constitutional compromise in that. You get your day in court and a hearing. If it's determined you are here illegally, you get deported. If you committed a crime or crimes, you can't get asylum or a stay on your deportation. You gave that up the second you committed a criminal act.