According to a Rasmussen poll taken on 2/14 and 2/15, just 27% of Americans say that the unfortunate incident "raises serious questions about his ability to serve as Vice President".
On the other hand, 57% say it was "just one of those very embarrassing things that happens to all of us."
66% say they've been following the news on this "somewhat or very closely."
And, 36% view Dick Cheney favorably, with 41% unfavorably disposed.
Even though they wouldn't matter in this case, apparently they asked about gun control laws too. 39% they should be stricter, with 52% disagreeing.