The merger of two white dwarfs may be preceded by the ejection of some mass in tidal tails, creating a circumstellar medium around the system. We consider the variety of observational signatures from this material, which depend on the lag time between the start of the merger and the ultimate explosion (assuming one occurs) of the system in a Type Ia supernova. If the time lag is fairly short, the interaction of the supernova ejecta with the tails could lead to detectable shock emission at radio, optical, and/or x-ray wavelengths. At somewhat later times, the tails produce relatively broad NaID absorption lines with velocity widths of order the white dwarf escape speed ($sim 1000$ kms). That none of these signatures have been detected in normal SNe Ia constrains the lag time to be either very short ($lesssim 100$ s) or fairly long ($gtrsim 100$ yr). If the tails have expanded and cooled over timescales $sim 10^4$ yr, they could be observable through narrow NaID and CaII H&K absorption lines in the spectra, which are seen in some fraction of SNe Ia. Using a combination of 3D and 1D hydrodynamical codes, we model the mass-loss from tidal interactions in binary systems, and the subsequent interactions with the interstellar medium, which produce a slow-moving, dense shell of gas. We synthesize NaID line profiles by ray-casting through this shell, and show that in some circumstances tidal tails could be responsible for narrow absorptions similar to those observed.