It depends on "who" catches you. If you are caught by the Border Patrol or U.S. Customs and Immigration Service they would probably deport you immediately. If the police arrest you, they have no power to deport you. If you commit a felony and are convicted you can, however, be deported.
It depends on why you don't have a green card. If it expired, then they will most likely give you an opportunity to appeal to the courts as to why you should be allowed to stay. If you are here illegally, then you will probably get deported. Unless you can prove that you are in danger if you return.
You could be deported, but in all actuality, you won't be unless you are involved in illegal activity or live in a place where they are trying to make examples of people who are here without the proper papers. While waiting for your papers to come through, make sure you stay below the radar as much as you can.