If you have a demographic model of twitter users and appropriately re-weight, why is this a bad approach to take?
I'm not claiming that such a model is guaranteed to be perfect or even as good as a pollster, but it sounds in principle like a reasonable thing to do, if you take appropriate precautions to reduce bias.
Now given the Twitters nature then is there such a model that is even approximately accurate?
Or in other words, what relevant data Twitters collects and how accurate it is?