How long do I have to sign a contract from my employer?

Any party to a potential contract can put a time limit on the other parties acceptance and that includes an employment related contract. Therefore, your employer could lawfully say "sign this contract by tomorrow or _____."  Assuming you are an employee-at-will like most in Tennessee, the _______ could be termination.  The exception to this would be if you are over 40 and signing a release of claims, i.e. a severance agreement, in which case you would be given either 21 days or 45 days depending on the situation.