In a wide-ranging phone interview from Madison on Thursday night, Mr. Walker sounded exhausted but joyful after his third statewide election since 2010. The governor laid out how he thinks center-right reformers can succeed among Democratic-leaning bodies politic—Wisconsin hasn’t broken for a Republican presidential candidate since 1984, when he was in high school—and why he doesn’t think the same trend is inexorable in like-minded states in 2016.

The race Mr. Walker won this week was close-run and became a referendum on his first term. His opponent, Mary Burke, a former executive of Trek Bicycle Corp., ran as a not-Walker. The governor calls her “almost the bionic candidate,” in the sense that her intelligence, business experience, gender and noncommittal up-the-middle platform were focus-group-tested as the perfect foil for his agenda and his track record of the past few years.

In June 2012, Mr. Walker became the only governor in American history to survive a recall election—initiated to reverse his enormously controversial 2011 budget-repair bill, Act 10, which limited the collective-bargaining powers of public-employee unions, as well as automatic dues collection and health and pension benefits. Big Labor and national Democrats returned this year to avenge their loss, though the irony was that Ms. Burke declined to relitigate Act 10 or even take a coherent position. The election turned on competing accounts of economic progress under Mr. Walker, such as job creation and rising household incomes.