Few things you could do:

1) take that extra class during the summer. Look at nearby institutions if your school doesn't offer the course during summer. Graduate at the end of the summer and start the job with the OPT.

2). Ask your employer to defer the offer until December, explaining although you really really (put emphasis) want to work for him/her, you may not be able to start until december. Departmetns can run without an employee for several months. If they really want you, they will wait.

3) Although quite unlikely, you could work out a deal between you and your boss. One could be like this: you will work full time, but get paid only for 20 hours plus a fat bonus at the end of the year for being an "extraordinary emploee."