Hmm.... there are a couple things that come to my mind. Were you drinking caffeine prior to the liquid diet? The other thing is while it is a liquid diet and you are most likely getting your fluids in, are you in fact getting 64+ oz daily? Those are the only two things that are coming to my mind currently. Good luck with this and I hope the headache goes away soon!
Another thought is that your body is going through carb detox. Sometimes when we reduce carbs significantly, it can give us headaches and/or flu-like symptoms. It's not pleasant but it will pass in a few days.
I had headaches for almost a week when I was on the liquid diet. I think the withdrawal from coffee, sugar, diet soda was the cause. It will get better just stay hydrated.