If it's coupled with a bill that basically prevents the US Government from going tits up he'll be forced to sign it. That or congress with vote for an override within an hour.

Riders are a very large check on the veto power. A president may only:
1. Sign the bill within 10 days (excluding Sundays).
2. Veto the bill within 10 days and send it back to congress with a message.
3. Do nothing for the 10 days.
a. If congress is in session bill becomes law.
b. Is congress is not in session the bill dies in a pocket veto. Since congress tends to hold pro-forma sessions this really only applies to bills passed December 24-January 2nd on an even year since the bill's 10th day after passage falls into a new session of congress.