I guess my original statement was incorrect, as they CAN assign you flying on X or off days per the PWA...thanks JugHead! I stand by my assertion that you DO NOT have to accept flying on X days or scheduled off days. This is taken directly from the scheduling handbook:

A pilot’s obligation to accept a trip on X days or regular line off days is not absolute, regardless of whether the trip is or is not a proffer. A variety of circumstances might prevent a pilot from accepting a trip.
For example:
• Not being physically located so as to be able to report.
• Having recently consumed alcohol.
• Lack of available child care.
• Lack of available transportation.
• Not being adequately rested. For example:
 A pilot, not on call, notified of a rotation with a report time within 10 hours should consider if he is sufficiently rested to accept the scheduled rotation.
 A pilot is not required to accept an inverse assignment that does not allow for 10 hours of rest between acknowledgement and report time for the assigned rotation.
Be polite and professional in your dealings with Delta personnel. If necessary, call your Chief Pilot for assistance.