I'm voting on a mouse being the cause. When the blower came on, it panicked and jumped into the squirrel cage blower wheel. He's dead by now and you'll need to remove him before he gets smelly.
I had that happen to my car a few years ago. Everything was fine when I turned it off to go into a store and do some shopping. 1/2 hour later when I came out, the dash shook so bad I had to turn the blower off. I had been using the a/c and had the blower on high. I stopped at a Walmart and bought a set of tools so I could get him out before we roasted. Darn little varmint!