Actually, Willie Brown was never referred to by the name "Slick Willie" while he was in state office.

There was nothing at all slick about him then. He was an arrogant, mean spirited, cutthroat, pushy, bulldozer of a politician, when he ran the state assembly. You did things his way, or you found yourself chewing sand in a ditch somewhere (figuratively) - especially if you were of his own political party. He was so hated by so many that there was a catchy slogan about him, used by both democrats and republicans in Sacramento; "If it's brown, flush it down!" Term Limits, was aimed mostly at him - personally!

Perhaps someone applied that nickname to him after he wormed his way in as mayor of San Francisco, where he had finally learned some finesse (could've been seen as slickness). But the real Slick Willie was already in the White House and his nickname known worldwide by then.