One of my friend whose visa would expire in 3 weeks re-entered US  without any problems. Even if you have atleast one day valid visa while you are at the port of entry, you will be allowed to enter US. 

However, your passport should not expire within six months. You should have valid I-20 signed on the third page  by International Student Advisor or someone of similar post at your University, the signature should not be older than one year during your return. 
I hope this helps!