No, he doesn't. That being said, I've wondered why the president doesn't use his bully-pulpit more effectively. Veto the pork-laden transportation bill on live TV and then read off the top 20 most expensive pieces of pork and explain why they are pork.
He thinks he'll pay a political price among voters and Congressmen if he actually tries to cut spending. That's why it keeps going up. He knows this stuff is pork, and everyone in Washington would prefer to pass it and not talk about it. Brave senators like Coburn an exception.