Events of the past week may offer a glimpse of what lies ahead for the GOP and for a beleaguered president and his party. Two Ohio ballot propositions showed the Buckeye State remains a bellwether of American politics. Sixty-one percent of Ohioans overturned Republican Gov. John Kasich's efforts to rein in public-employee unions, handing labor (a vital part of President Obama's political base) an important victory. It was also a significant loss for Mr. Kasich.

A recent Quinnipiac poll suggested why the package went down. True, Ohioans backed making public employees pay at least 15% of health-insurance premiums (60% favor, 33% opposed) and contribute at least 10% of wages for their pensions (by 57%-34%). However, respondents opposed restraints on public-employee unions, including a ban on strikes and limits on collective bargaining over health benefits. As many as one out of every five Republicans opposed Mr. Kasich's reforms, perhaps because police and firemen were covered by them.

On the same day they turned down union reform, however, 66% of Ohioans voted to pass a state constitutional amendment saying citizens can't be forced to purchase health insurance—in other words, to defy the "individual mandate" in Mr. Obama's health reform. The vote, while symbolic, is a strong signal that ObamaCare remains deeply unpopular.

Moreover, Republicans on Tuesday gained control of the state Senate in the critical battleground of Virginia and won the Mississippi House for the first time since Reconstruction. Republicans now dominate 61 of the nation's 99 state legislative chambers. (Nebraska has a unicameral system.)

On the presidential front, Herman Cain's responses to charges of sexual harassment are drawing questions about his sure-footedness. He and his campaign have made several false accusations and had to revise their initial story regarding Mr. Cain's knowledge of the charges. Mr. Cain needs to press the National Restaurant Association to release reports he says will exonerate him of the first two complaints. The controversy is now too big to be resolved by declarations of innocence, no matter how passionate.

Karl Rove is a former senior adviser and deputy chief of staff to President George W. Bush. He is a Fox News contributor and author of "Courage and Consequence" (Threshold Editions, 2010). To continue reading his column in The Wall Street Journal, click here

Karl Rove joined Fox News Channel as a political contributor in February 2008. He also currently serves as a columnist for the Wall Street Journal. Mr. Rove helped organize the political-action committee American Crossroads. His latest book is "The Triumph of William McKinley: Why the Election of 1896 Still Matters" (Simon & Schuster, 2015). Follow him on Twitter @KarlRove.