According to this article linked from the wikipedia article, there is an absolute upper limit of how much protein your body can process into "burnable" glucose each day. This is around 1600 calories a day, which is a starvation ration.

So don't bother eating more than 1600 calories worth of lean meat per day and try to make up the rest with plants, fat or snickers bars.

But here's the question: Is it better to glean a few calories from plants each day or just fast completely?

Over the short term of a day or two, I'd think that any calories at all will be helpful in keeping your glucose level up. Over the medium term (days to weeks), does eating a little bit disrupt the "fasting mode" your body uses to draw from your fat reserves? Over the long term (month+), of course, you will eventually run out of reserves, so every little bit helps.