If it came down to health reasons, Tsongas would probably resign before he was forced to endure the embarrassment of being forced out of office. For Tsongas to be removed, there needs to be some sort of event that makes it obvious that he can't continue on as President. If not, the Democrats would probably be able to cover it up enough that it doesn't come to the fore. Maybe he collapses at a special function, or maybe he pulls a Bushu-suru and vomits on a foreign dignitary.
But let's say Tsongas rapidly declines to the extent that he is incapacitated and unable to resign because he's comatose or something. At that point, Congress goes through the motions, and, say, Dick Gephardt becomes President. The right wing media would probably repeatedly question Tsongas' capabilities, but once he falls ill and the 25th is invoked, everyone will probably play softball for the first year (especially of Tsongas dies) before things go back to normal.