I went there last night and saw that the standard AC plug that comes out of the furnace and plugs into an outlet in the closet was scorched and they likely smelled the burning plastic.
This was not an over-current issue as the blower motor has a fuse in the line inside the furnace (something I put in about 1987 and it has never blown). I think it was just a crappy outlet that was making poor contact on the hot and neutral and it was arcing every time the blower motor turned on.
I thought it rather strange that the AC for the furnace was using a regular cord rather than being directly connected to the AC supply with wires inside flexible conduit, but I replaced the AC socket put in a new cord from the junction box inside the furnace (rather than attaching a new plug to the existing wire).
I'm thinking of going back and directly wiring it into the outlet box, though the current plug/socket arrangement has worked since it was built about 30 years ago.
Is it normal for the AC power for a gas furnace to be connected with a plug/socket? It's not like that in my own house.