A "veto message" is a statement or letter from a person in power, like a president or governor, explaining why they are rejecting or refusing to approve a law or decision. Full definition
Mr. Paterson spent long stretches of Thursday hand - signing veto messages on the first of some 6,900 earmarks before him. (nytimes.com)
One of his typical veto messages called for the development of «a comprehensive approach to this issue within the broader context of New York State's law enforcement needs, rather than addressing the needs of local government units in an ad hoc matter.» (politico.com)
Buchanan reports that when he was serving under Reagan he oversaw the president's «veto messages killing legislation to protect the shoe and textile industries. (religion-online.org)