Could be a minor out of balance condition with one of the tires, or a minor alignment issue that is unnoticeable at lower speeds. Also the tires may not be rated for the speeds you are attempting and are distorting.
Another possibility is a harmonic imbalance, the tread of the tires may create a noise that causes a wobble in the steering, the sound is always there but raises to a harmful pitch at a certain speed.
You probably need to get your tires balanced. Or replaced. If the bias goes (steel belt breaks or shifts), the car will waddle at low speeds, and the steering wheel will shake at high speeds.
== == Bad Tire or Tires.
Tire out of balance, bent wheel, drive shaft bent, loose or worn steering parts.
Either your drums or rotors are out of round.
The tires are out of balance...may need tires, or rim(s) are bent
Check the entire front end. Wheel bearings, ball joints and tie rod ends can all wear and call this problem.
have front suspension checked
wheel balance is out.if it jerks alot at high speeds possibly a tire seperation.if those two possibilities check out then check the toe angle of the front suspension.
Mine did it because of a horrible alignment
You rotors are warped and will need replaced/resurfaced.
Could be out of balance Tire may be worn and need replacement Could be a bent wheel
go get 2 new tires and have the alignment checked on it