Even if SHA-256 is partially broken (say easier to find hashes, but not fully broken), you-d see major resistance from ASIC miners. You might even get a split network.
I don't think this is a coherent argument.
If some SHA-256 break makes it easier to find hashes, the difficulty will just go up and the network will be just as secure. Existing ASICs will be obsolete and will be replaced by new ASICs that take advantage of this break.
You'd need something that broke the difficulty mechanism for it to matter. It's almost inconeivable that there'd be a SHA-256 break such that adding more zero bits to the beginning of the hash didn't make them much harder to find. So the probability of this happening is near zero.
Any other break wouldn't require changing the mining algorithm. So long as difficulty still serves to measure work done, the mining need not change. And nobody has a stronger incentive than miners to fix any other problems with the system, and this is only going to increase.
Once the majority of mining power comes from ASICs, miners will have a huge investment in expensive equipment that is good for nothing but producing Bitcoins. Miners would be very quick to work to fix any defect that threatened the value of Bitcoins.
