Did Republicans win so many of the elections on Tuesday because of their conservative base or because they went beyond it? The answer to both questions is yes.

In some places in 2009 it was enough to not be a Democrat, just as it was sufficient for Barack Obama to be an alternative to President George W. Bush in 2008. In Greensboro, N.C., an unknown 70-year-old conservative who has never held elective office beat the incumbent mayor, the first such defeat there since 1973. Message to Republicans: When only 20 percent of Americans self-identify as Republicans, it is not our brand voters are buying. It’s the other guy’s brand they are rejecting.

Republicans won, fundamentally, because President Obama and the Democratic leadership in Washington have rebranded...