Well, according to Einstein's description of gravity this may not be such an issue as you think. The Earth's movements are, after all, governed by gravity. Now gravity doesn't so much "curve" an object's course, as it bends spacetime around the object's path (which is a straight line).
And you're here on the Earth's surface, so you're moving along the same line. You hop in your car, start deviating from the straight-line path by 88mph, and then... what, exactly?
Your post (and many people's intuition) assumes that you suddenly change velocity in all dimensions, so that you move in time but stay at a fixed position in space. The problem is, the concept of a "fixed point in space" is a figment of human imagination; there's no such thing. A fixed point in space implies a prefered frame of reference, and there simply is no such thing.
So what spacial trajectory does the time machine follow? Well, why would it not continue moving at 88mph deviation from the straight-line path through curved spacetime that it's already following - that being the same line being followed by the Earth?
Gravity would cause the time machine to "follow" the Earth as it moved through time. Not the Earth's gravity, as many other posters have suggested, but rather the Sun's gravity and the other various forces that move the Earth.
There are many, many, many problems with time-travel fiction, but the idea that you would be lost in space just isn't one of them.