The thing is I don't have the drive to start the assignments early
I only take action a day before the deadline and before you call me a lazy dog I'm compulsively conscientious when it comes to studies. It's just that I lack motivation

Consider in the future... you risk not only a bad grade like now... but risk getting fired for missing a deadline once too often.

That can be just one extra bit of info that can help you break the habbit. Most employers would be far less forgiving than your College professor would be.

My mother says, "Do it now and get it over with, so you'll have lots of time to play."

Can you reward yourself with something if you get an assignment done on time/early?

Count how many days between when the assignment was given and when it is due. Put that many dollar bills inside a jar or box. Each day that passes and you don't work on the project, your roommate (or whoever) gets a dollar. Each day you work on the assignment, you get a dollar. Of course, there will have to be rules set up so you don't cheat. For instance, a third person is in charge of the money jar and doles it out dollar by dollar/day by day.

If you wish, use five dollar bills or tens -- but make it something you want and don't want to lose.

Sorry, no if you really cared for your lessons you would start early, use a calender, set up plans and follow it