A substantial fraction of the mass of a giant molecular cloud (GMC) in the Galaxy is confined to clumps which occupy a small fraction of the volume of the cloud. A majority of the clumps in several well-studied GMCs (Ophiuchus, Orion G, Rosette, Cepheus OB3) are not in gravitational virial equilibrium, but instead are confined by the pressure of the surrounding medium. These clumps thus violate one of 'Larson's (1981) laws'. Generalizing the standard virial analysis for spherical clouds to spheroidal clouds, we determine the Jeans mass and the magnetic critical mass for the clumps in these clouds. The Alfven Mach number, which is proportional to the internal velocity dispersion of the clumps divided by the Alfven velocity, is estimated to be of order unity for all the clumps. The more massive clumps, which are in gravitational virial equilibrium, are too massive to be supported by magnetic fields alone (i.e., they are magnetically supercritical). Internally generated turbulence must play a key role in supporting these clumps.