  We explore the role of soft gluon exchange in heavy quarkonium production at
large transverse momentum. We find uncanceled infrared poles at NNLO that are
not matched by conventional NRQCD matrix elements. We show, however, that gauge
invariance and factorization require that conventional NRQCD production
operators be modified to include nonabelian phases or Wilson lines. With
appropriately modified operators, factorization is restored at NNLO. We also
argue that, in the absence of special cancellations, infrared poles at yet
higher orders may require the inclusion of additional nonlocal operators, not
present in the NRQCD expansion in relative veloctiy.
