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The electrification of heavy-duty vehicles (HDEVs) is a nascent and rapidly emerging avenue for decarbonization of the transportation sector. In this paper, we examine the impacts of increased vehicle electrification on the power grid infrastructure, with particular focus on HDEVs. We utilize a synthetic representation of the 2000-bus Texas transmission grid, and realistic representations of multiple distribution grids in Travis county, Texas, as well as transit data pertaining to HDEVs, to uncover the consequences of HDEV electrification, and expose the limitations imposed by existing electric grid infrastructure. Our analysis reveals that grid-wide voltage problems that are spatiotemporally correlated with the mobility of HDEVs may occur even at modest penetration levels. In fact, we find that as little as 11% of heavy duty vehicles in Texas charging simultaneously can lead to significant voltage violations on the transmission network that compromise grid reliability. Furthermore, we find that just a few dozen EVs charging simultaneously can lead to voltage violations at the distribution level.