False. I'm 25 with a fiancee. If both of us lost our jobs we would have the mortgage paid through December already. Taxes are taken care of in the escrow account. I have a 6-month "just in case" savings that I will never touch, and we have plenty more savings that although might have been intended for spending at a later date (renovations, new car), they would be able to be used.
Would I need a new job eventually? Yes. I would want one asap so I don't have to touch savings. Hell, if I wanted I could milk it without a job for as long as possible.
Do I NEED a new job immediately? FALSE.