In order to examine the possibility that dust effects cause color gradients in elliptical galaxies, we have constructed a set of elliptical galaxy models spanning a wide range of dust properties, including mass, spatial distribution, and spectral properties. These models are spherically symmetric and include the effects of scattering. We have calculated the emergent broadband colors from the far-UV bands through K: These results were then compared with the color properties for a sample of 52 galaxies taken from the literature. In the optical, we can reproduce the magnitude, morphology, and color gradient ratios [i.e., Delta U-R)/Delta(B-R)] observed in many of the galaxies. The best fits are found for distributions with rho(d) similar to r(-1) and tau - 1, which corresponds to dust masses on the order of 10(6) M(.) within the central 10-30 kpc. More condensed dust profiles also produce strong color gradients, but only in the central regions (r < 0.5 kpc). For many of the objects in this sample, the implied dust masses are in reasonable agreement with the dust masses inferred from IRAS observations, although a number of objects require significantly higher dust masses than their IRAS observations imply if their color properties are to be attributed solely to reddening by dust. Our models suggest that a simple dusty elliptical galaxy scenario can reproduce the magnitude, morphology, and ratios of observed broadband color gradients in many ellipticals. We find that currently available color gradient measurements are consistent with our model results but that these measurements are not precise enough in many objects to provide tight constraints on the models. Extended dust distributions will greatly complicate the interpretation of all broadband data. Any broadband analysis hindered by age-metallicity degeneracy will also be hindered by dust effects. In effect, all broadband observations of elliptical galaxies may be age-metallicity-dust degenerate. We also consider the effects of dust on several global relationships in ellipticals, such as the color-magnitude relation and various distance indicators.