Lease Renewal, how long can you wait?

I live in a large rental building and am considering moving to a new place. My lease is up 5/31. My management company sent me letter on 2/8 with a new lease saying "please return within 60 days," which would be 4/8. I really would like more time to look for a new place, but don't want to miss out on staying at this rent if I cant find anything better. My question is, if I don't renew within the 60 days, is that deal off the table so to speak. Can I just stall them and then if I don't find something better, send in the new lease, say, on 5/15? Thanks, stressing out!