How old is your dog and what exactly does she do when she's eating? Are you feeding kibble (hard food) or soft (or both)? Does she display the same action with both foods?
Does she do it every time?
I think you're right on ! It sounds like she could have a gum infection or even an abcess somewhere. If she'll let you really look around in there, start at one side (in her mouth) and run your finger along the gumline (from the jawline to front), then the other side. Do the same with the bottom and then repeat from the underside. You should either feel or see something yourself, or she'll let you know when you hit it.
Whether she's cooperative or not, you need to take her to her vet. A tooth or gum problem isn't something you can deal with on your own and if not treated soon enough, it could become rather serious and very complicated to treat.
The good thing is that she's still interested in trying to eat and she's getting her fluids. Until you can get her into the vet (Monday?), try offering her the soft foods she likes, boiled and pulled apart meats with rice and broth, peanut butter on whole wheat bread, etc..
There are of course other possible causes for this behavior and intestinal problems are among them, so seeing her doctor is pretty important.
Keep an eye on her and monitor her behavior. If you notice labored breathing, loss of balance, inability to get up or excessive pacing, vomiting, diarrhea (any blood in the vomit or diarrhea), distress or fever - get her seen immediately.
Here is a checklist for her behaviors that will be helpful, but by no means all there is. Your instincts are your best guide! http://www.purina.ca/dogs/health.asp?article=137