The Centers for Medicare and Medicaid Services (CMS) in the federal government is hiring product managers (I believe its the first time that CMS has posted with this position title).
It's in WOODLAWN, MARYLAND, but some of the multiple openings at CMS won't require in office work most days of the week. The role would work for people that are relatively junior (with at least one year of professional experience), but there's also room for someone senior to make a big mark at an agency that processes the 1.5 billion/day in Medicare payments, in addition to supporting Medicaid, CHIP, and many other services.