If an alien is caught in the US by law enforcement and is not carrying his/her passport w/I-94 or I551 (green card) he/she can be booked for a misdemeanor. Driving license will not do it.

Visitors who intend to stay in the US for <180 days are allowed to drive in most states with the driving license of the country they are normally resident in, provided they have an additional translation document (aka International Driving Permit) that is acceptable as per the Article 24 of the United Nations Convention on Road Traffic (1949).

But then it is in the law enforcement agency discretion. If you are dealing with a township policeman catching you for speeding, a county sheriff in front of whom you just made a abrupt lane change or a CBP officer doing spot checks near the AZ/Mexcio border (all of the above happened to me), all ask/look for different papers.

Know your laws and be aware of them.