[shorod]

Your problem is likely caused by a warped rotor. Warped front rotors will usually cause the steering wheel to shake as you describe. Warped rotors on the rear (if your Taurus has 4-wheel disc brakes) will often times be felt strongest in the brake pedal.

However, since you mention that the problem sometimes doesn't appear until after a few minutes of driving after sitting overnight, be sure to have the front end checked for worn suspension components, mainly ball joints and tie rod ends (both inner and outer).

What year is your Taurus?

-Rod