Let me add my voice to the chorus of "I remember my first week" singers.
When I started, my plan was to ride to the transit station 2.5 miles away and back in the evening. I gave it a test run after work one evening. I made it out half a mile and realized that if I didn't head back then I wouldn't make it back. When I got home, I could barely stand up.
But I kept at it, and within a week, I was making it to the transit station. Within a month, I was skipping the transit station once a week and going the entire 11 miles to work. Now, two years later I'm commuting 110 miles a week, riding centuries on the weekends and doing cyclocross races in the fall.
One other reminiscences... Even once I was making the entire 11 miles, the rolling hills were killing me. In fact, it used to irk me hearing people call them rolling hills because they were kicking my butt. One hill in particular, I'd crawl up in my lowest gear and have to stop and take a breather for a few minutes before going on. Yesterday I took that hill at 20 mph.
Did I mention that I was 37 years old, overweight and obscenely out of shape when I started this?
So, yeah, stick with it and you'll find you can do it in no time.
+1 on the rest days. You can get there without that, but it will take a lot longer.