I don't think this was the case at all. I seem to remember that his poll numbers were surprisingly low in that hypothetical Senate match-up.
Giuliani and Clinton were at a 41-43% dead heat before Giuliani announced that he had cancer. Interestingly, if Pataki had entered the race instead, he did better than Giuliani beating Clinton 46-41. Had Clinton lost that race, I believe that would have been the end of her.
BTW, this poll was at the height of his marital troubles. Even without 9/11, Giuliani's personal image has rebounded significantly since then.