The intention is that if you go through the entire deck without finding all the cards you're supposed to dig for, you get as many as you found and the action ends.
That can actually happen in rush mode, too, if the cards you need are in players' hands. Note however that there are 2 copies of each gem combination, so you've got pretty good odds of finding what you need unless you're near the end of a crisis mode game.
You can examine the burned cards to check whether you've already burned both copies, if you like.
Thank you Jeremy! That's how I played it!
I haven't had the chance to play "Rush Mode" yet. In fact I have only played solo and I think it's one of the top three solo games I have played. Highly addictive!!!