According to my current understanding of how Bitcoin works (admittedly sketchy), if SHA-256 is broken in such a way as to decrease the difficulty of computation by (say) 5 orders of magnitude, then the difficulty factor could be adjusted by 5 orders of magnitude.   Same way it responds if a bunch of fast machines start generating blocks all of a sudden, only measured in orders of magnitude instead of just a factor of two or five or so. 

I guess the "breaking" part comes in because the Byzantine agreement part would fail since a guy who is secretly breaking Bitcoin's SHA-256 would be dominating the "computing power" and thus have more than the 50% of the resources needed to forge transactions?