When you say, "my family helped me get that money...I feel like I shouldnt risk their money," do you mean that your family helped to co-sign your loan or act as guarantors? If that is the case, then no, you really should pay off the debt. And idlewords is right, you can use the time to learn about working in a team. Or even network to find cofounders. From your statement "I've been thinking I might try for YC", I'm guessing perhaps you haven't found co-founders yet? Paul Graham's essays tend to stress the importance of good co-founders.
But if they helped you get the loans in some way that doesn't involve their credit getting damaged should you fall behind on payments, maybe you should talk to a financial counselor about options, like consolidating loans or asking for a forbearance due to unemployment/hardship. That's going to make your loan principal grow very large though.
So I also think that working for a few years to pay off the loans is the best idea because then you can focus on your startup without the stress of looming monthly loan payments on top of earning no salary whilst developing, but perhaps you should ask someone who can give more specific advice. Not to sound harsh, but it seems that by asking internet boards, you're looking for a way to alleviate your conscience, both to yourself (in terms of your life ambitions) and to your family (in expectations and finance). Don't worry too much Good luck with whatever decision you make!