Sudden large amount of thick white/yellow liquid pouring from vagina mixed with rubbery ovulationlike substance. not aroused. poured out in one "push"?

Need to be examined: That doesn't sound normal, and i'd guess you have an infection of some kind, but you'd need to see a doctor to be sure. If no fever or pain, it can wait until the office opens.

Did you recently: Have unprotected sex? The sperm and seminal fluid doesn't really have any place to go, but back out the way it came. It can kind of look like a weird congealed whitish rubbery discharge. If you haven't had unprotected sex, then we'd have to look for a different answer. The first is prevented by showering after sex and using your fingers and water to get any remaining goo out. Condoms catch goo!