I think it would be really hard to start out at that distance and keep it up every day. The first day isn't so bad, but it'll wear on you as the week goes on. Plus you'll have occasional thunder storms, strong wind, driving rain, freezing rain, and snow to deal with. That's quite different than riding on a warm, sunny day. Don't get me wrong, commuting is great fun, especially when you get to the point where it's no longer tiring and you welcome the challenges that mother nature throws at you, but that kind of conditioning takes months (at a minimum) to build up.

You may want to pick and choose the best cycling days for now, maybe once or twice per week until you get used to it. When that gets easy, try riding on a few "iffy" days (where rain or strong wind is in the forecast). Make it a goal to do one full 5-day week by the end of the summer. As the weather turns colder again, try to keep riding as late into the season as you can, but keep your options open. Commuting by bike will be much more fun if you don't torture yourself.