When Steven Law was deputy secretary of labor in the George W. Bush administration, he routinely scrutinized the disclosure forms of labor unions. Unions had recently been required to report new details about how they spent their members' dues money. Mr. Law discovered that organized labor was contributing millions to a variety of liberal groups—environmentalists, gay-rights advocates and left-wing blogs, among others.

For Mr. Law, it was a revelation and a lesson. He concluded that the labor movement had enlarged and strengthened...