I just had a 93 N/A come up with the issue you are describing, and unfortunately, there are two possibilities here... one involves the worn bearing described by others. having a machinist remanufacture the rods and shaft can be expensive.
"two" involves a loose shaft which I've been told can be caused in a 3800 series 1 by the retention mechanism wearing through the front valve cover. this is much easier to fix. I'm pretty sure your year would have this sort of retention. My 93 Bonne' was not so lucky, and now I have one reconditioned engine from a company called Jasper.
Water pump failure will probably be the last thing to check. It isn't likely on your car, and the RPMs will be different also.
Pray for "two." I know this is late, but hopefully still useful. By the way, if this car was driven like this for awhile, more than likely it should have thrown the rod already, so keep hope alive!