In 1995, a Harris Poll asked: "Would you say you are a better than average driver, an average driver or worse than average?"
54% said better, 40% average, and only 1% worse (most of the remaining 5% didn't drive)
People have a pretty high estimate of their abilities in most areas, so the general pattern isn't surprising. But a 1965 Gallup Poll makes an interesting comparison:
"In general, how do you rate yourself as a driver--better than average, average, or not up to average?"
36% said better, 62% average, and 2% not up to average (non-drivers were not asked)
The question wordings weren't identical, but I don't see any reason that they should produce different responses, so it looks like Americans' estimate of their own driving ability became substantially more favorable over the thirty years.