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Recent deep millimeter-wave surveys attempt to measure the carbon monoxide(CO) luminosity function and mean molecular gas density through blinddetections of CO emission lines. While the cosmic star formation rate densityis now constrained in fields hundreds of arcmin$^2$ or more, molecular gasstudies have been limited to $\le50$ arcmin$^2$. These small fields result insignificant biases that have not been accounted for in published results. Toquantify these biases, we assign CO luminosities to halos in cosmologicalsimulations to produce mock observations for a range of field sizes. We findthat fields $\lesssim 10$ arcmin$^2$ alter the recovered shape of theluminosity function, causing underestimates of the number of bright objects.Our models suggest that current surveys are sensitive enough to detect sourcesresponsible for approximately half of the cosmic molecular gas density at highredshift. However, uncertainties in the gas density measurement are large, andcosmic variance may double the uncertainty claimed in these surveys. As aresult, the field size needed to detect redshift evolution in the molecular gasat high confidence may be more than an order of magnitude larger than whatcurrent surveys have achieved. Shot power intensity mapping measurements areparticularly sensitive to Poisson variance and require yet larger areas toconstrain the gas density or its evolution. We provide a simple prescriptionfor approximating uncertainty in total CO emission as a function of survey areaand redshift, for both direct detection and intensity mapping surveys.

Biases and Cosmic Variance in Molecular Gas Abundance Measurements