It looks as though I'm going to have to eat my words. It's in Wiktionary, among other places:
"push off
3. (transitive) To delay, postpone, put off, push back."
http://en.wiktionary.org/wiki/push_off
And yes, there are other examples when you look. Moral: look it up before you sound off. It's still unfamiliar to me, and I strongly suspect it's a hybrid of "put off" and "push back", but there it is. It seems to be used mostly in the sense of "stave off": delay something inevitable but undesirable, as in the Fledermaus quotation, or in "the European Central Bank (ECB) will attempt to push off the day of reckoning".