Using Dremel without motor brushes
If you run a carbon brush motor on the metal springs, you'll destroy the commutator (part where the brushes contact the rotor.)

A GOOD hardware store or hobby shop may have brushes in stock you can purchase today, rather than awaiting delivery. Otherwise, if you are desperate to continue, buy another dremel (or similar), rather than destroying the one you have and THEN buying another. Either way you'll buy one, but one way you have two after your brushes come.

It's also a good idea to buy a spare set of brushes so you have a set on hand the NEXT time this happens - when you install them, order another set of spares - that way you never have to wait for delivery to get up and running again.