I do not think it is fair to say "the Higgs looks like it's going to be at higher energies then anticipated". In fact, my money was on 160 GeV, based on models coming from noncommutative geometry. But the basic constraints on the Higgs mass from the standard model were really not very good (the following comes from the review article of Djouadi, 0503172v2). Short story: Unitarity starts failing around 900 GeV, perturbation theory fails around 700 GeV. A lower bound can be gotten by requiring that the Higgs quartic coupling remain positive, which gives $M_H> 70$ GeV. This depends on the cutoff-scale; the 70 GeV comes from assuming a 1 TeV cutoff scale. If the SM is valid up to GUT scales, this rises to $M_H>130$ GeV.
So, although the current values for Higgs are actually just below that 130 GeV, I think it's not fair to make any statement except that "it seems fine for the standard model" - it's too early to say "the Higgs mass implies new physics". All of these estimates are based on measured parameters such as the Top mass, which has it's own uncertainty associated with it. There is also the fine-tuning problem, but the above bounds generally give the same or slightly better estimates then that.
If someone wants to mention SUSY implications of a $\sim 125$ GeV Higgs, be my guest - there certainly are some. But SUSY can't possibly be real anyway, so I'm ok not knowing them ;-)