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 \mu m , and H \alpha images to measure the CO line ratios , molecular gas masses , and instantaneous gas depletion times . For three galaxies in our sample ( NGC 4254 , NGC4321 , and NGC 4569 ) , we obtain molecular gas masses of 7 \times 10 ^ { 8 } -3 \times 10 ^ { 9 } M _ { \odot } 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 \mu m emission ; however , much of the central luminosity in this galaxy may be due to the presence of a central AGN .