We present high-resolution CO(1-0) observations of the lensed submillimeter galaxy (SMG) SMM J14011+0252 at z=2.6. Comparison to the previously-detected CO(3-2) line gives an intensity ratio of r_3,1=0.97+/-0.16 in temperature units, larger than is typical for SMGs but within the range seen in the low-z ultraluminous infrared galaxy population. Combining our new data with previous mid-J CO observations, we perform a single-phase large velocity gradient (LVG) analysis to constrain the physical conditions of the molecular gas. Acceptable models have significant degeneracies between parameters, even when we rule out all models that produce optically thin emission, but we find that the bulk of the molecular gas has T_kin=20-60 K, n_{H_2}~10^4-10^5 cm^-3, and N_CO/Delta-v=10^{17.00+/-0.25} cm^-2 km^-1 s. For our best-fit models to self-consistently recover a typical CO-to-H_2 abundance and a plausible degree of virialization, the local velocity gradient in the molecular gas must be substantially larger than its galaxy-wide average. This conclusion is consistent with a scenario in which SMM J14011+0252 has a fairly face-on orientation and a molecular ISM composed of many unresolved clouds. Using previous H-alpha observations, we find that SMM J14011+0252 has a spatially resolved star formation rate vs. molecular gas surface density relation inconsistent with those of normal local star-forming galaxies, even if we adopt a local disk-like CO-to-H_2 conversion factor as motivated by our LVG analysis. This discrepancy supports the inference of a star formation relation for high-z starbursts distinct from the local relation that is not solely due to differing choices of gas mass conversion factor.
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