Might the LHC see nothing new at all? There's no guarantee that supersymmetry (or more exotic new physics) will be seen at the LHC. Meanwhile, it's standard lore that a Higgsless standard model becomes nonunitary somewhere in the vicinity of 1 TeV. Are we at least guaranteed to get some positive information about new physics, in the form of deviations from the predictions of this "higgsless standard model"? 
 A: It is possible that the LHC could find just a standard model scalar Higgs. It would have to fit in the windows between 135 GeV and 157 GeV or 173 GeV to 185 GeV. In this case no new physics is needed and other effects such as large CP violations and dark matter go unexplained.
If it is below 135 GeV the standard model would predict an instability of the vacuum so something else such as SUSY would have to be there to correct. This would already be indirect evidence for beyond standard model physics, but it is just about possible that the new physics would not be seen yet.
A Higgs mass above 185 GeV is inconsistent with other measurements, but only when assuming the standard model applies, so again a heavy Higgs would be indirect evidence of new physics. There is no certainty that the new physics would be seen.
If the Higgs was excluded over all its mass range that would also be an indication of beyond standard model physics. It would mean one of two things, either the Higgs really does not exists and something else would have to be breaking electro-weak symmetry, or the Higgs exists but some new physics hides it from us, e.g. it may have a dominant decay mode into new particles that form jets that are hard to see against the background. Such scenarios are possible but it would be as if Nature was being devious to make life awkward for us.
Something needs to explain dark matter but that could easily be a particle with mass 10 TeV, or a lighter particle that does not interact strongly enough with standrd model particles to be seen at the LHC.
So in short, yes it is quite possible that nothing, or just the standard Higgs may be seen. 
A: The LHC opens a new frontier in energy exploration. The results will be "new" by definition, as with all explorations. Now whether there will be dragons, tigers or just moose is something we have to wait for.
If we enter a desert as far as specific new resonances/particles go, which are predicted by various models, that will also be new physics information. Supersymmetry will disappear on the horizon, the Higgs will be rescued by composite Higg models until the next machine and higher energy levels are explored. This rescue will come, because the Standard Model has been very successful in encapsulating all known high energy data.
In my opinion we will find new physics, maybe unexpected, but new. Already the asymmetry in the jets of top production at the Tevatron is an indication that something new is going on at high energies. The researchers have to keep an open mind, not run after two and three sigma deviations, be very careful in systematic error estimates, and "something is coming , don't know what, ought to be grand" as the song from the west side story says.
