Computer Security Question Barack periodically

Barack periodically comes up with brilliant ideas to stop the financial crisis, provide health care to every citizen, and save the polar bears. He wants to share these ideas with all the cabinet members but also get credit for the ideas. Extending the above approach, he shares a secret key K with all the cabinet members. Next, he broadcasts each idea z followed by value h(k||z). Does this approach work or can Tim claim that he came up with the ideas instead of Barrack, Justify your answer.