Non competes are interpreted and enforced under state law. For this reason, you really should consult with local counsel. Having said that, I have to assume that there is no way to enforce a no compete that the person refuses to sign.
Most employers ask employee to sign as soon as they start because how do you get someone to sign after they are laid off. If you sign now, what is the "consideration" you are getting? You need consideration for most contracts to be enforceable.
Maybe you are getting special severance benefits? They must be dangling some incentive to make you sign now?
There may be some important facts missing. Thats why I have to again stress this is probably a case where you should consult with local counsel.