We explore the origin of the color-magnitude relation (CMR) of early-type galaxies in the Virgo Cluster using spectra of very high signal-to-noise ratio for six elliptical galaxies selected along the CMR. The data are analyzed using a new evolutionary stellar population synthesis model to generate galaxy spectra at the resolution given by their velocity dispersions. In particular, we use a new age indicator that is virtually free of the effects of metallicity. We find that the luminosity-weighted mean ages of Virgo ellipticals are greater than ~8 Gyr and show no clear trend with galaxy luminosity. We also find a positive correlation of metallicity with luminosity, color, and velocity dispersion. We conclude that the CMR is driven primarily by a luminosity-metallicity correlation. However, not all elements increase equally with the total metallicity, and we speculate that the CMR may be driven by both a total metallicity increase and a systematic departure from solar abundance ratios of some elements along the CMR. A full understanding of the role played by the total metallicity, abundance ratios, and age in generating the CMR requires the analysis of spectra of very high quality, such as those reported here, for a larger number of galaxies in Virgo and other clusters.