  Mott insulators with both spin and orbital degeneracy are pertinent to a
large number of transition metal oxides. The intertwined spin and orbital
fluctuations can lead to rather exotic phases such as quantum spin-orbital
liquids. Here we consider two-component (spin 1/2) fermionic atoms with strong
repulsive interactions on the $p$-band of the optical square lattice. We derive
the spin-orbital exchange for quarter filling of the $p$-band when the density
fluctuations are suppressed, and show it frustrates the development of long
range spin order. Exact diagonalization indicates a spin-disordered ground
state with ferro-orbital order. The system dynamically decouples into
individual Heisenberg spin chains, each realizing a Luttinger liquid accessible
at higher temperatures compared to atoms confined to the $s$-band.
