Mike, I am writing this with a smile on my face. What you describe, is exactly what is happening to me, honest. You could be my twin brother.
I overcame (so to speak) this "I can't do it" feeling and the nervousness associated with it, and played in front of others 2 times. (cheers from everyone

)
There were a number of reasons for this:
1) Simply, there was an opportunity to do so. I can't say "hey, I am going to play you something" out of the blue.
2) There was another active guitar player in the room in both of these occasions, meaning that I was playing WITH someone else and not FOR an audience. Simply put, I "offloaded" some of my psycological burden to the other player, (not literally, but I felt this way) so (in my mind again) I was not the center of attention.
3) I WANTED to do so. If you don't want it, you won't do it.
4) In the second occasion, which involved an audience of about 10-15 persons, there was whiskey involved

. You get the idea. Not completely drunk, not sober either. Enough to push me forward.
5) I had confidence, (took me 9 years of playing to myself of course) that I could cope, even if I never played the songs, just seeing some chords in a piece of paper. Of course I had heard the songs before. It is not much difficult to "play along" with a guitar player, by playing some chords with the left hand and some very simple arpeggios or melodies on top with the right.
6) I thought to myself (here's the whiskey helping): If you finally don't play vey well, so what???? Nobody's gonna die.
So, work with what you have....you want to do it, right??? find an opportunity, share the burden with someone else, play what you can, and lace it all up with booze. You can't, and you won't fail.
Best of luck,
Theodore
P.S. You made a VERY important step, by writing this after lurking for some time.... You just performed, in front of strangers, and explained your "problem". If you think of it, performing in front of family and friends who know and love you is much easier, isn't it?.