The IceCube neutrino discovery presents an opportunity to answer long-standing questions in high-energy astrophysics. For their own sake and relations to other processes, it is important to understand neutrinos arising from the Milky Way, which should have an accompanying flux of gamma rays. Examining Fermi TeV data, and applying other constraints up to >1 PeV, it appears implausible that the Galactic fraction of the IceCube flux is large, though could be present at some level. We address Sgr A*, where the TeV-PeV neutrinos may outrun gamma rays due to gamma-gamma opacity, and further implications, including dark matter and cosmic-ray electrons.