Tuesday's elections, which produced a resounding Republican victory in New Jersey and a dispiriting loss for the GOP in Virginia, highlighted the challenges ahead for a badly divided party — and will probably intensify an internal debate about how to win back the White House in 2016.

At a time when the party's image has sunk to record lows nationally, the results of the gubernatorial elections will reverberate far beyond the borders of Virginia and New Jersey. Off-year elections are hardly foolproof in predicting the future, but as GOP leaders digest what happened Tuesday, the lessons they take away from the races after their autumn of discontent will shape the coming rounds.

In New Jersey, Republican Gov. Chris Christie rolled to re-election by a margin that will make him a leading contender for his party's presidential nomination in 2016, should he decide to run. His victory in a solidly blue state will be touted as a model for a party that needs to expand its coalition in national campaigns. But will the formula Christie employed in New Jersey work in Republican primaries and caucuses or in a national election for president?