It really depends on what your current status in the US is (is your I-94 expired, etc) and what is the reason for the denial of your application for adjustment of status on the basis of marriage.  If you are now out of status and unlawfully present (i-94 expired) and the adjustment of status has been denied, you may actually have removal proceedings started against you.  If your application has been denied but you are submitting motions to reopen/reconsider, etc. during that time, you should be allowed to get your driver's license.  You need to provide more details about the specifics of your situation and perhaps it might be a good idea for you to consult with an immigration attorney.  Good luck.