Most government legal jobs will probably not consider graduates of either school. I recently worked a government law office in California and all of the recent hires were either former interns from ABA schools or experienced attorneys from ABA schools. Hiring is so competitive right now that government offices have the luxury of being very picky.
If a Taft or Concord grad passed the baby bar, passed the bar, worked solo for, say, five years and built up lots of good trial and transactional experience, then applied to government job . . . well, maybe. Still a longshot. I would contact each school and ask how many graduates are working in government.
I don't know where the OP is located, but many ABA and all CBE school offer part-time programs for students who work full time. I started law school in my early thirties with a family, a mortgage, the works. I'll graduate from an ABA part-time program in a few weeks. It is a grind, but it can be done!