If Monica had come forward of her own volition and complained about Bill's misogyny, he would have had to go. But, you must remember that it didn't go down that way at all.
The fact is that the GOP/Scaife, et al spent eight years and millions and millions of dollars investigating Clinton for anything they could dream of.
Along he way, Clinton picked up more and more sympathy and support among voters because he seemed likeable and competent enough and times were good and got better through most of his term of office. His approval rating was never below 50 after 1995, for nearly his last 5 years in office. Like Obama, it was well over 60 at the end of his second term. By the time the House impeached him, the GOP Senate was too cowardly to act, since Clinton was so popular.
I think Clinton's popularity also was, in large part, due to the fact that the public faces of the GOP lynch mob (Gingrich, Ken Starr) came across as such sweaty-palmed weirdos in comparison to the smiling and affable Bill. But that's just my opinion.