Elections matter. House Republican Leader Eric Cantor’s stunning re-election defeat probably scuttles any hope for an immigration overhaul this year.

Nervous House Republicans: Cheer up. Instead of fretting over Cantor’s loss, study the resounding victory by another Republican, South Carolina Sen. Lindsey Graham.

Cantor lost his conservative Virginia district to political novice David Brat, a tea party-aligned college professor who repeatedly accused Cantor – falsely – of supporting “amnesty” for the undocumented.

Graham won a resounding 56 percent of the vote in his very conservative state against six farther-right wing challengers who tagged him with labels like “Grahamnesty.”

How did Graham win while Cantor lost? By embracing the Senate’s bipartisan comprehensive immigration reform bill, which he co-authored and Cantor voted against.

Graham has been arguing openly and tirelessly for an immigration overhaul since 2006. He has pointed to his work with Democrats on immigration as evidence of his willingness to solve tough problems, partisan differences. The big lesson to be learned from Graham’s victory: Voters will accept a difference of opinion, but they hate hypocrisy. Where you stand in politics is often less decisive than how well you show voters that, despite differences, you’re still on their side.

Contrary to some election night commentaries, there were plenty of other reasons for Cantor’s defeat. Bad polling, which showed him ahead by more than 30 percentage points, stands out.

So does a widespread perception that he had lost touch with his constituents and snuggled up too cozily with financial elites. Cantor’s attack ads against Brat backfired by raising the challenger’s profile and informing voters they had an alternative choice. Charges of sabotage by Democratic crossover voters proved to be ungrounded. It was a base election, and turnout was 50 percent higher than two years ago, most of it coming from voters newly drawn into the district by Republican state lawmakers.

For what it’s worth, polling by the left-leaning firm Public Policy Polling and liberal advocacy group Americans United for Change found high support for the tenets of immigration reform, despite high opposition to anything that sounds like amnesty for those here illegally.

More than 70 percent of registered Republican voters in Cantor’s district told those liberal group’s pollsters on primary election day that they supported reforms to secure the borders, block employers from hiring those here illegally and allow undocumented residents without criminal backgrounds to gain legal status.

Those issues, plus the stickier issue of a pathway to citizenship, are central tenets in the immigration reforms that Graham defended and discussed frequently at campaign stops.

Immigration welled up in recent weeks on conservative talk radio and talk shows, partly sparked by a recent and tragic surge of undocumented and mostly Central American children crossing our border with Mexico and seeking asylum.

But Graham, having talked immigration reform since 2006, sounded better prepared to address the issue directly than Cantor, whose efforts to carve out a middle ground came off as waffling or flip-flopping to be all things to all people.

He voted against the DREAM Act, for example, that would open college opportunities to children bought here illegally after birth, then he signaled support for a scaled-back version – that he never brought to the House floor for a vote.

Apart from immigration, it is important to note, Graham is about as resolutely critical of the Obama administration as his fellow maverick Republican pal Sen. John McCain of Arizona, particularly on the hot buttons of foreign policy, national security and the administration’s handling of the terrorist raid in Benghazi.

Republicans trying to bring peace to their internal establishment civil war should study the differences between the Cantor and Graham contests. Unlike Cantor, Graham put himself clearly on the side of an immigration overhaul and come out looking like a winner.