We got a video a while back in which Meatloaf spent an evening with about 30 or 40 fans. one of the questions asked was the one you posed.
He said that everyone asked the same question... What is "That"? At this point he gets out a blackboard and writes the choruses, underlining each of the first lines and says "That is what I won't do":
I won't;
- Forget the way you feel right now
- Forgive myself if we dont go all the way - Tonight
- Stop dreaming of you everynight of my life - No Way -
And of course at the end of the song where there is the dialog sequence and it closes with him saying would never screw around and leave her, but this is the finale, the build-up is the other promises he makes through the song.
Like most of the Steinman and Meatloaf collaborations, the song is extremely well constructed and while the choruses and verses are similar, they do not repeat.
Bit pedantic aren't I? Bet you can't tell I'm a bit of a fan, either?