The problem is, you're already starting in the hole by buying a brand new bike. And that's just the beginning. It's an expensive hobby, and you don't really find that out until after you sink all that money into the initial purchase and start reading forums and browsing bike shops seeing all the things that you "need."

35 miles/day, just quit smoking, on your feet all day, 4 am, out of shape... (You didn't actually say out of shape, but you'll find out in a week how badly out of shape you really are.) Yes you can do it, but IMHO, the odds are stacked against you keeping it up long enough to pay off that bike and really start saving money.

I have been commuting 16 miles/day for a year and I am just now to the point where I can do it every day without wishing someone would give me a ride in when I roll out of bed. I know that if I had a car available to drive, there is no way I would have the motivation to ride every day.

I'm not saying that you shouldn't try, but I don't think you'll save enough money to make that a good motivator unless you can give up the car altogether. There are enough other benefits in cycling to make it worthwhile without the monetary savings.