I have had this and other problems with my Droids. I'm on my 4th Droid now and I started experiencing the headphone jack problem after a couple of days.
I cut a small portion of a plastic straw and wedged it between the 1/8th" jack housing and the frame of the phone, so far so good. Hopefully this droid won't be giving me any problems now.
I would very strongly recommend against using anything permanent like epoxy. Not only could this damage the phone, but should some other manufacturing defect crop up Verizon/Motorola could use your modifications to the phone to tell you your warranty has been voided. Using a straw seems like the best solution as it is durable and easily pulled out (paper will rip) and is of sufficient thickness.