Most of the time I ride a touring bike on my commute, which is only a mile longer than yours, but in the summer I don't hesitate riding my road bike. I ride on some fairly messy roads, with broken pavement, sand washouts, etc. I do look for flat resistent tires, or use Spinskin liners. If your bike takes 26" or 700 tires I strongly recommend Specialized Armadillios. If you need 650's you a limited to the Continentals and Schwalbe touring tires, or Spinskins. If you are concerned about the cost of changing tires, just change your rear tire. Front flats are less common, and are quicker and easier to do. If you have fairly new tires, consider the Spinskins.

If you are riding your good road bike, besides a good and secure place to lock it up, you do need to avoid heavy rain. I haven't damaged my frame, but I have ruined a rim by being forced into a puddle by traffic and hitting a pot-hole the puddle had hidden.

Commuting offers many opportunities for training. I tend to hammer my way to work in the morning, then return home at a more casual pace, on a longer route. I arrive at work well energized and get home de-stressed. Don't let tires keep you from trying commuting. Good luck.