Not saying this happens to everyone but it is possible to get over qualified and if the job market isn't good, private businesses wont' want to hire you because they are required to pay you more than someone with just a 4 year degree but can do the job just as well as you can.
The reason I bring this up is because I know someone who got a PhD in mechanical engineering, he said he would have been fine if he would have just went to get a job after getting his 4 year degree. Then later went to get his masters and PhD while working at the same time.
Now he's finally gotten into a job, at a University, but is getting very low pay as a Programmer. Thats all they had open in the department, he also had to work for free in the Bio-Mech department to get into the "system". It just never occurred to me that being overqualified could also cause problems.