Who were Christ's most ardent enemies while he walked the earth? Without any doubt, the Jewish religious leaders ("the Jews," in most translations) were his enemies. And yet, Christ excoriated them time and time again, calling them snakes and vipers, whitewashed sepulchers, and sons of the Devil. Love? You betcha! Not the namby-pamby "love" that's so in vogue nowadays.
If we could only do as well in following His example.
He also called on God to forgive them as they tortured him to death. The concept of loving the sinner is certainly biblical because that was Christ's whole mission and the concept of hating the sin was taught by Christ; so the love the sin, hate the sinner thing is absolutely biblical. I don't recall that is was originally posted by Salvation as a verse quote in the first place.