Who are they? I don't know the answer, but I suspect Senator Byrd (born Nov. 20, 1917) and Justice Stevens (born April 20, 1920) are right up there. I haven't checked the House of Representatives, though.
Post your answers in the comments, with birthdays (exact or approximate) and pointers to sources supporting your claim. I'm looking for current employees, not past ones. I'm also looking for full-time employees, not retired or semiretired ones.