I'd venture to guess that you can do it or build yourself up to it. One thing I would suggest is that you make sure your bike fits you properly, meaning the seat is at the right height and setback, the handlebars are in a good position for you, etc.

I started commuting last January. My trial ride was on MLK day, so I didn't have a time deadline. I made the commute successfully, though I had to stop a few times for breaks. My commute is 13.5 miles each way, and I was quite sore by the end of my ride home. I later discovered that some minor adjustments to my bike allowed my legs to be more efficient. The sore leg problems I was having improved, and the commute quickly became easier.

I now do the commute 3-5 times per week with ease and have lost a considerable amount of weight. I'm in the best shape I've ever been in, and I save well over a tank of gasoline each month by leaving the car parked at home. Commuting by bike has been one of the best decisions I've made.