We present results from spectroscopic observations with the Michigan/Magellan Fiber System (M2FS) of 147 stellar targets along the line of sight to the newly discovered "ultrafaint" stellar systems Tucana 2 (Tuc 2) and Grus 1 (Gru 1). Based on simultaneous estimates of line of sight velocity and stellar-atmospheric parameters, we identify 8 and 7 stars as probable members of Tuc 2 and and Gru 1, respectively. Our sample for Tuc 2 is sufficient to resolve an internal velocity dispersion of 8.6^+4.4^_-2.7_km/s about a mean of -129.1+/-3.5km/s (solar rest frame), and to estimate a mean metallicity of [Fe/H]=-2.23^+0.18^_-0.12_. These results place Tuc 2 on chemodynamical scaling relations followed by dwarf galaxies, suggesting a dominant dark matter component with dynamical mass 2.7^+3.1^_-1.3_x10^6^M_{sun}_ enclosed within the central ~160pc, and dynamical mass-to-light ratio 1913^+2234^_-950_M_{sun}_/L_{nu},{sun}_. For Gru 1 we estimate a mean velocity of -140.5^+2.4^_-1.6_km/s and a mean metallicity of [Fe/H]=-1.42^+0.55^_-0.42_ but our sample does not resolve Gru 1's velocity dispersion. The radial coordinates of Tuc 2 and Gru 1 in Galactic phase space suggest that their orbits are among the most energetic within a distance of <~300pc. Moreover, their proximity to each other in this space arises naturally if both objects are trailing the Large Magellanic Cloud.