Jogee, yes, of course it will be a problem if your visa is expired. Even though you have a valid I20 but if you're visa is expired, they might not allow you to enter U.S according to the USCIS website. But until and unless you have a valid I20 and valid visa, doesn't matter how many days or month left, they should allow you to enter U.S. If i were you, i would take suggestion with my school international advisor/DSO.