I tried to address this elsewhere (also in response to Ira). But to quickly rehash, my reasoning goes as follows (this is somewhat technical): if the Higgs mass is >> the W boson mass, partial wave unitarity is violated. So we know the Higgs mass must be <~ 1 TeV for the Standard Model to work. But otherwise, with the Higgs mass put in by hand, the SM is renormalizable, and so, reading it as an Effective Field Theory, it doesn't predict it's own demise. Of course, we know that gravity becomes strong near the Planck scale, and so one would expect problems to begin at very high energies. While there remain a) many inadequacies with the Standard Model and b) many alternative theories that extend the Standard Model, the Standard Model has been tested exhaustively, and so far, there is nothing to indicate additional operators. This is why, if the Higgs mass is successfully added experimentally without revealing any problems with the theory, my bets are that we won't find any additions to the SM at LHC energies. And this is why I argue that we should hope *not* to find the Standard Model Higgs, but to find something else instead.

I can also clarify: there’s a common abuse of language that I’m trying to avoid. When I say “Standard Model Higgs,” I mean a Higgs that behaves in such a way that the Standard Model is renormalizable, without modification or extension. Many people use “Higgs” to refer to whatever particle moderates electroweak symmetry breaking. If the Higgs, in this generalized sense, requires modification to the minimal Standard Model, then there’s definitely good reason to think the LHC could resolve some of the SM’s inadequacies. I would argue that, strictly from an EFT perspective, the fact that the SM doesn't seem like a complete picture is also indirect evidence that the electroweak symmetry breaking mechanism can’t be simple. Which, I think, is why so much physics beyond the SM concentrates on exotic symmetry breaking. Yet, if it is simple, it's hard to see where new physics will fit in at LHC energies. This is where the "negligible" remark enters.

Of course, there won't be any telling what the LHC will find until the LHC is turned on (further delays mentioned today in Nature).