What happens if a house rejects a bill that was introduced by a member? The bill can only be reintroduced in the other house.
The bill moves to the other house for a vote.
The bill must be reintroduced in the next legislative session.
The bill must go through the legislative process again.

A two-thirds vote or greater is needed in both the House and the Senate to override the President's veto. If two-thirds of both houses of Congress vote successfully to override the veto, the bill becomes a law. If the House and Senate do not override the veto, the bill "dies" and does not become a law.

If he breaks the law then he had to resign from his post and so he'll lose his/her powers.