I would venture to suggest that the reason you have difficulty committing words to memory is because you are used to resorting to the song book. You have no incentive to learn the words.

I find the best way to learn a song is to sing it. Make sure you know and understand the story the song is telling. Sing it through a few times with the words and then try it without. You won't remember it all, so go back to the book to fill in the gaps, and try again. Repeat as necessary until you've got it all. Then keep singing it - in the car, in the shower - until it's fixed.

I find the worst way is to try to learn a line at a time, like we learned poetry at school. Learn it as a story, as a whole, rather than thinking of it as a succession of words you have to learn.

Don't worry about getting it word-perfect, either. As long as you're telling the story right, and have got any key words and phrased right, it usually doesn't matter too much if you begin a line with "and" or "but".

I'm with those who believe you have a responsibility to the song, to the audience, and to yourself to be properly prepared. That means learning the song. If you're properly prepared, you'll be more confident and less likely to make mistakes. If you need a few prompt cards, fine, but use them discreetly.