The off-year elections were, in two big races, an unmistakable rebuke of Democrats, reshuffling Obama’s political circumstances in ways likely to have severe near-term consequences for his policy agenda and larger governing strategy.

Independents took flight from Democrats. They suffered humiliating gubernatorial losses in traditionally Democratic New Jersey, where Obama lent his prestige in a pair of eleventh-hour campaign rallies Sunday, and in Virginia, which had been trending leftward and just last year was held up as an example of how Obama was redrawing the political map in his favor.