I don't know anything about the judge that denied your son's request for a court appointed attorney, but the law states that the State must appoint an attorney for indigent defendants. However, this rule only applies to defendants who may suffer jail time if convicted. It is likely thatt he judge has already decided that he will not jail your son if he pleads guilty. Assuming that this is his first offense, the prosecutor will probably offer him a plea to a reduced charge of Operating While Visibly Impaired. It carries fewer points on his driving record, lower fines, he won't suffer a suspended license (though he will be restricted for 90 days) and his driver responsibility fees will be lower. Bottom line is that the court did not appoint a lawyer because he knows he is not going to incarcerate your son. Make sure that he asks the prosecutor for a plea to impaired driving. He should be fine. Let me know if you have any further questions, I'll see if I can help.
It is critical that your son obtain an attorney. He should beg and borrow from friends and family and consult with other legitimate sources of funding to come up with money for an attorney. In the event it is completely impossible for him to retain counsel, try calling the local bar association and see if they can assist you with someone locally that would consider taking the case pro bono, or at a very reduced rate.
Is this case pending in Marquette? I would be happy to provide you with a free consultation, and answer questions you may have about the process. Please contact me if you would like to discuss this matter further.