Since you are married son of a U.S. citizen, you are not considered an "immediate relative" under the immigration laws. Only immediate relatives are eligible for "Adjustment of Status" ("Green card") if they are out of status in the U.S. You are in Third Preference Category (F3 - married sons/daughters of US citizens), and depending on which country you are from, the priority date for you is probably several years away (you can check the priority dates on the visa bulletin here). So since by the time your priority date becomes current, you would certainly be out of status, and not being an "immediate relative" you would not be eligible for Adjustment of Status. So if you can avoid being out of status (especially, to avoid the 3 and 10 year bars to reentry), you shouldn't remain in the U.S. without a non-immigrant status.
Answered on Sep 27th, 2013 at 10:55 AM