The neighbors might think (But, baby, it's bad out there)
Say, what's in this drink? (No cabs to be had out there)
I wish I knew how (Your eyes are like starlight now)
To break the spell (I'll take your hat, your hair looks swell)
OK, this is where shit gets intense. Re: "Say what's in this drink?" and "I wish I knew how to break the spell" -- what kind of fucked-up Rohypnol/love potion mash-up did this dude dose her with?! Is that Christmas tree in the corner getting a little blurry? And “No cabs to be had out there” -- how would he even know that? He's basically telling her she is trapped and will be forced to hear lines like, "Your eyes are like starlight now," possibly for the rest of her life. It's like hearing an episode of Dateline unfurling before our ears.
I ought to say no, no, no, sir (Mind if I move in closer?)
At least I'm gonna say that I tried (What's the sense of hurtin' my pride?)
I really can't stay (Oh, baby, don't hold out)
Ah, but it's cold outside (Baby, it's cold outside)
No means no, right? Then wouldn't "no no no" mean triple no? Finally, in a fit of short-term Stockholm syndrome, she kind of just gives up and says, "At least I'm going to say that I tried" -- meaning he has fully succeeded in breaking her spirit with a messed-up alchemy of peer pressure, alcohol, and cheese-tastic flattery. Lord knows what else he's been mixing in there.
I simply must go (But, baby, it's cold outside)
The answer is no (But, baby, it's cold outside)
This welcome has been (How lucky that you dropped in)
So nice and warm (Look out that window at that storm)
"The answer is no" is a pretty straightforward way of saying no, in my experience.