While it would be very surprising if the Higgs turned out to be a boring, Standard-Model Higgs, there are very good reasons to believe that something Higgs-like has to happen at the multi-TeV scale. Basically, without a Higgs the Standard Model yields non-physical predictions (e.g. probabilities for certain processes exceed unity).

In other words, the Standard Model isn't even consistent above a TeV or so without the Higgs. Something has to give.

Edit: to make contact with your example, everyone knew that if you didn't find evidence for the ether, than the model of electromagnetism was very wrong. In fact, that was great justification for carrying out Michelson-Morely type experiments.