The furnace thing turned out to be (after they replaced all the likely furnace parts) my water heater. Which is an 80 gallon tank so it's a couple thousand to replace. The company has been lollygagging around with this whole thing. They last came out Friday to take pictures of the old tank that I had to get me a replacement. They said they'd get me a quote ASAP.
Because you should always get a second quote, I called around. The first guy was rude, like I was interrupting him, and abruptly asked if he could call me back that afternoon at my number. Of course. Haven't heard back from him. That was Friday morning.
This problem of not being able to get laborers to work at my house is a recurring thing and has been for years. Many up here complain they're out of work and poor, yet trying to actually get someone to perform work is akin to a miracle, sometimes.
Anyway, the furnace guy showed me how to turn the water heater on and off so the furnace wouldn't drip a lot when it was off and I wouldn't have to empty the bladder. Turn it on when you want hot water. Not a huge deal, a little inconvenient. I asked him how long this bandaid would work, and he said a long time. This morning I turn the handles to turn it back on, go to crawl in the shower and discover now we have no hot water.
Now I'm pissed.