We discuss constraints on the rates of stirring and dissipation of MHD turbulence in molecular clouds. Recent MHD simulations suggest that turbulence in clouds decays rapidly, thus providing a significant source of energy input, particularly if driven at small scales by, for example, bipolar outflows. We quantify the heating rates by combining the line-width-size relations, which describe global cloud properties, with numerically determined dissipation rates. We argue that if cloud turbulence is driven on small internal scales, the ¹²CO flux (enhanced by emission from weakly supersonic shocks) will be much larger than observed; this, in turn, would imply excitation temperatures significantly above observed values. We reach two conclusions: (1) small-scale driving by bipolar outflows cannot possibly account for cloud support and yield long-lived clouds unless the published MHD dissipation rates are seriously overestimated, and (2) driving on large scales (comparable to the cloud size) is much more viable from an energetic standpoint, and if the actual net dissipation rate is only slightly lower than what current MHD simulations estimate, then the observationally inferred lifetimes and apparent virial equilibrium of molecular clouds can be explained.