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Based on what you described above, I would say that it's most likely the induced draft motor bearings. If this is the case, you'll likely be looking at a couple to a few hundred dollars to replace (likely around $200-300).
It is also possible that the relay for the induced draft motor has pitted contacts and is buzzing. If this is the case, the buzzing won't stop after 40 seconds, but bay get drowned out by the blower.
Now that I see what you said in the Already Tried section, I'm almost certain you'll need a new induced draft motor. It will be better to go ahead and replace rather than wait until the motor fails on a cold night.
There is no safety concern as the pressure switch has to close before the furnace will fire up. The pressure switch can't close if the induced draft motor isn't running.
You can wait a week, but it's impossible to say if it will last until then. It may fail next time it starts, or it could work for another 2 years... hard to say.
If it fails, the furnace will completely shut down and there will be no heat.