There have only ever been two impeachments of Presidents since the United States of America was founded in 1776. One was Andrew Johnson in 1868, and the other Bill Clinton. Seeing as though this is such an exclusive club, and Bill Clinton's scandal began what some call the "information age", an age where any information is accessible to the public via the Internet, it is very likely the scandal will never be forgotten.
Yes, we will always think of Monica when we think of Bill, because you can't think about a Bill Clinton presidency without thinking of all the women that he harassed and took advantage of. Just like you can't think of Nixon without thinking of Watergate. Clinton did a lot of good things, but they are overshadowed by his bad behavior.
Yes, Bill's (Clinton) affair with Monica will forever be in our minds as it was since a well-documented public event that caused individuals to re-think their opinion on him. However, many also feel that his indiscretions with Monica were personal and did not relate to his job as President of the United States.
Despite the affair with Monica Lewinsky during his presidency, Bill Clinton did a lot for the United States. There are people who only remember this and his "lying" to a grand jury, but these people are typically only in the news media. When you ask a person on the street "Who is Bill Clinton?" They may start talking about his support of Obama in 2008, or how Hilary inspired the Affordable Care Act. The American people do not define Bill Clinton by his single public blunder, we are not that shallow.