This song has become somewhat controversial, with many people arguing that it's a song about date rape, or is at least coercive and rapey (see here, for example). According to Wikipedia, the conversation that the song consists of is marked in the score by the notations "mouse" and "wolf," corresponding, of course to "woman" and "man." That sure does look like prey and predator. The song has been done with the roles reversed, by Betty Garrat and Red Skelton (you have to get through the Esther Williams/Ricardo Montalban video before Betty and Red come on) and it's been performed on Glee by two men. Still, it's inarguable that the song was intended to be sung, and is almost always sung, by mouse/woman and wolf/man.
It's true that the man is very persistent. And I'd be willing to go as far as saying that it's this kind of thing that contributes to the idea that when a woman says no, she doesn't really mean no--she just needs to be talked into whatever the man wants of her. Also, the line "What's the sense in hurting my pride?" (wolf) makes me absolutely cringe.
And yet. There are lines in the song that indicate that the female half of the duo isn't all that unwilling to stay: "maybe just a half a drink more," "maybe just a cigarette more," "I ought to say no" (notice that "ought"), "at least I'm gonna say that I tried," etc. A lot depends on just who performs the song: much can be conveyed by the particular singer.
Anyway, feminist though I am, I like this laid-back version by Norah Jones and Willie Nelson.