IN the space of a long weekend, the Republican Party became the party of immigrant ambition. And it’s not just Arnold Schwarzenegger — it’s Bobby Jindal too. Schwarzenegger is a great symbol of America, the land of opportunity. He came here from Austria as a young man, became the most famous body-builder ever, became a move star despite his thick accent and married into the Kennedy dynasty. And now he’s been elected governor of America’s most populous state.

Schwarzenegger said he was running to pay back America and California for the success he had enjoyed: “I came to California 35 years ago because I saw this state as the best place on earth to fulfill my dreams.…

“There were times people said it could never be done, that an Austrian farm boy can come over to America and get into the movie business and be successful in the movie business. They said, ‘We cannot pronounce your name, you cannot speak English well and your body’s overdeveloped.’ And you know what happened? I became the highest-paid entertainer in the world, OK?”

His story was improbable enough to impress even the French: “American democracy has tremendous resilience,” said French Interior Minister Nicolas Sarkozy. “Someone who’s a foreigner in his country, who has an unpronounceable name and can become governor of the biggest American state — that’s not nothing.”

But Oct. 4, far from the bright lights of Hollywood and the national media spotlight, 32-year-old Indian-American Bobby Jindal led the all-party primary for governor of Louisiana.

Talk about assimilation — Jindal’s so American that at age 4 he told his parents he wanted to be called Bobby, like the youngest of “The Brady Bunch,” rather than his given name of Piyush.

He still faces a tough runoff with Lt. Gov. Kathleen Blanco on Nov. 15. But if he wins, he’ll be another star and another symbol of American openness and opportunity.

And his future could be even more promising than Schwarzenegger’s. His mother was pregnant when his parents arrived in Baton Rouge from India, so he’s a natural-born citizen and eligible to run for president — once he’s 35. Watch for the Republican Party to feature him as a symbol of America and of the GOP’s welcoming approach to minorities.

Schwarzenegger and Jindal both campaigned as fiscal conservatives. They part company on some social issues. Jindal, a convert to Catholicism, runs radio ads attacking abortion, gay marriage and Hollywood and supporting the display of the Ten Commandments. Schwarzenegger opposes gay marriage but says, “I do believe that gay couples are entitled to full protection under the law and should not be discriminated against based on their relationship.” And he’s unlikely to lead any crusades against sex and drugs.

This plainly reflect the different electorates of Louisiana and California. Schwarzenegger’s combination of fiscal conservatism and social tolerance seems more likely to gain a national audience. Perhaps an older Jindal, considering running for national office, will moderate his social conservatism.

In American politics, immigration is usually discussed as an issue for Hispanic voters, the largest group of recent immigrants. Schwarzenegger’s victory will give the Republicans cause for hope. Running against the state’s first Mexican-American candidate for governor, and promising to repeal a new law granting driver’s licenses to illegal immigrants, he still got 31 percent of the Hispanic vote.

Not every Republican has Arnold’s appeal, of course. But the possible combination of the Terminator and a brown-skinned Republican governor in the Deep South has real potential to shake up immigrant voting patterns.

At an international conference recently, I expressed skepticism about Schwarzenegger’s commitment to smaller government. Two Scandinavians and a Russian took sharp exception. “He’s an international hero,” they said, “and he’ll be a great symbol of American liberal values-freedom, opportunity, and free markets. You’d be crazy not to support him.”

Especially if Jindal wins, he and Arnold may go a long way toward improving the image of the Republican Party in America, and the image of America — land of freedom and opportunity — in Europe, Asia and the rest of the world.