How long can a female Culex (the type that transmits encephalitis, etc.) mosquito live without drinking blood?
According to this website, the answer depends on factors such as temperature, etc.
However, I think your question is a bit misleading… mosquitos do not live primarily on blood. IIRC (from a conversation years ago with my father, a forest entomologist), the primary source of nutrition for mosquitos is nectar from flowers, not blood. A female mosquito will try to get a blood meal before laying eggs so that the extra nutrition will improve the odds of the eggs hatching.
Again, though, that conversation was a long time ago…
I saw a quick segment on mosquitoes on a local environmental show here and they mentioned adult mosquitoes live for a month or so. Not sure how long they stay in larval form though…