By the time he ran for governor again in 2010, he was the establishment candidate. Still, Mr. Walker made sure not to get outflanked by primary opponent Mark Neumann, a former congressman campaigning on his willingness to buck the House GOP leadership.

After Mr. Neumann backed an Arizona law requiring police to check the status of anyone they thought might be illegal, Mr. Walker said he had “serious concerns” about the law. When his campaign Facebook page was instantly flooded with criticism from conservatives, Mr. Walker changed his mind that afternoon.

He also followed Mr. Neumann’s lead in opposing a state smoking ban, even though as Milwaukee County executive he had forbidden smoking outside county buildings, and his wife was, and remains, a fundraiser for the American Lung Association. After he won the election, he never sought to alter the smoking ban, and later declared it a success.

During his 2014 re-election campaign, Mr. Walker softened his tone on social issues. He aired a TV ad on abortion that touted legislation he supported that left “the final decision to a woman and her doctor,” and he declared the gay-marriage an issue “resolved” after a federal judge invalidated the state’s ban on same-sex weddings.

But in a February appearance before religious broadcasters in Nashville, Tenn., Mr. Walker hardened his rhetoric. “I think of strong families and I think it starts with a strong marriage,” which comprised a husband and a wife, he said. During the same speech, he stressed his opposition to abortion, noting that he carries in utero photographs of his two sons with him.