But Mr. Ryan has shown he’s not shy about firing back at the president, bringing both budget numbers and sharp rhetoric to the fight. “Rather than building bridges, he’s poisoning wells,” the usually mild-mannered Mr. Ryan said. “Exploiting people’s emotions of fear, envy and anxiety is not hope; it’s not change. It’s partisanship. We don’t need partisanship. We don’t need demagoguery. We need solutions. And we don’t need to keep punting to other people to make tough decisions.” Mr. Ryan’s first go-around with Mr. Obama came even before he became Budget Committee chairman. He was one of the Republicans invited...