The DoD (US Department Of Defense)
For the NHS and Walmart, there are credible looking websites saying 1.28 million. Manpower claim 2 million. It is not really clear what these numbers mean (full time equivalents, people on regular salaries or what?).
At any rate the old factoid about the NHS being the '3rd biggest employee after the red army and the Indian railways' looks slightly dubious (and different websites differ as to whether the factoid is talking about the Chinese or Russian red armies anyway).