First of all, particles of energies higher than 10^20eV have been observed in several experiments since the first observation in Utah in 1991. Just google for ultra high energy cosmic rays (UHECRs) or "oh my god particle". The existence of these particles above the GZK cut-off is not really a disputed fact.
The study and theoretical understanding of these UHECRs are in fact becoming a sub-field of its own today, and I have seen it come up again and again in the last couple of years at conferences.
The point here is that the GZK cut-off only applies to particles originating _very_ far away (more than 50 mega parsecs), since an UHECR produced "locally" could reach us without having a significant change to interact with the cosmic microwave background. The current theoretical puzzlement thus does not have to do with the observation of particles violating some fundamental law, but is due to the fact that people do not know of any "local" source in our neighbourhood which could produce particles of such high energies. There is certainly no indication that this affects the SM, and certainly not the big bang theory.
Of course, as a particle physicist, I would *hope* that the effects are due to physics beyond the SM, but I would guess it is more likely that the answer is going to be that we do not understand all astrophysical objects as well as we had hoped.