Is the finish intact? If so, it may be just a buildup of wax. Try washing it down with mineral spirits, then rub straight with the grain with 4/0 steel wool followed by Guardsman polish. If this doesn't quite do it, but the finish is still intact, you can try hand rubbing it as they did at the factory.

Wet the table top with mineral oil, Sand with 400 grit wet or dry paper on a rubber sanding block, be careful not to sand through on the edges. Wipe off the residue and repeat the operation with 500 grit wet or dry paper. Rub with 4/0 steel wool after cleaning off the sanding residue.
Polish with Guardsman polish.

If the finish is not intact, you need to refinish it.

Agree with Furnone. There is no saving a finish that has degraded to goo.

Here is a link that might be useful: http://www.homesteadfinishing.com/htdocs/savingfinish.htm

Thanks to both of you. I will try your suggestions. It's very difficult to actually see if the finish is intact at this point due to the thick gooey build up on top.