We present large-area maps of the CO J = 3-2 emission obtained at the James Clerk Maxwell Telescope for four spiral galaxies in the Virgo Cluster. We combine these data with published CO J = 1-0, 24 μm, and Hα images to measure the CO line ratios, molecular gas masses, and instantaneous gas depletion times. For three galaxies in our sample (NGC 4254, NGC 4321, and NGC 4569), we obtain molecular gas masses of 7 × 108 - 3 × 109 M sun and disk-averaged instantaneous gas depletion times of 1.1-1.7 Gyr. We argue that the CO J = 3-2 line is a better tracer of the dense star-forming molecular gas than the CO J = 1-0 line, as it shows a better correlation with the star formation rate surface density both within and between galaxies. NGC 4254 appears to have a larger star formation efficiency (smaller gas depletion time), perhaps because it is on its first passage through the Virgo Cluster. NGC 4569 shows a large-scale gradient in the gas properties traced by the CO J = 3-2/J = 1-0 line ratio, which suggests that its interaction with the intracluster medium is affecting the dense star-forming portion of the interstellar medium directly. The fourth galaxy in our sample, NGC 4579, has weak CO J = 3-2 emission despite having bright 24 μm emission; however, much of the central luminosity in this galaxy may be due to the presence of a central active galactic nucleus.