If this is a stupid response -- please forgive, but....

I had the screw cap part break off of one of my valves (definitely an "oh sh!t moment), and I was able to screw it back on. (the post itself was intact) I don't know if I just got really lucky, but it still works. I do have to be careful to gently unscrew the valve now, because it has come off a couple more times, but each time (after finding the @#!@ tiny little piece on the floor) was able to replace it.

Just wanted to share that -- it saved me from a tube change. You may be talking about a totally different kind of break, and if so, sorry for the simplistic response!

Christy