Well, I drove for a company out of Okemos, and the vehicle I drove would do the same thing, 60 to 65 it would vibrate. It would go through a set of steer tires in about 20K miles. I finally convinced the mechanic to install new front shocks. Vibration went away and I got 80K out of the set of new tires that went on at the same time.
I'm not saying that's what it is, but, it IS a very good possibility.