Why is my family less important than your product? This kind of micro thinking, writ large, is how we end up with busted policy at a macro level.
It is to your colleagues, to the founders, and to the investors, all of whom have a significant vested interest (no pun intended) in seeing the company succeed and have all taken various kinds of risks to invest in the company and product.
Simply put: the product/company will be feeding my family in the success case.
If the cost of carrying an employee -- not a cofounder! -- for three months (how much is that? 50K? 60K?) is going to kill the startup, you a) probably shouldn't have hired the person to begin with and b) don't have much of an startup to begin with.
It's continually amazing to me how, in a capital environment awash with cheap funds and outrageous valuations, this kind of cheapness pervades everyone's thought processes. Stop thinking like broke college students, and start thinking like the people of substantial affairs you claim to be.