Gov. Arnold Schwarzenegger, R-Calif.

California Gov. Arnold Schwarzenegger doesn’t understand the Republican Party if he thinks it can shift to the left on social issues without damaging its base, a traditional-family lobby group says.

“Schwarzenegger’s statements that the GOP party would not lose its base if it embraces gay marriage and abortion rights show extreme arrogance and total ignorance concerning the values and dedication of the party’s core constituents,” said Karen England of the Sacramento-based Capitol Resource Institute. “Schwarzenegger has spent too much time in Hollywood. He needs to start mingling more with mainstream Californians.”

Schwarzenegger’s remarks were published over the weekend in the German daily Sueddeutsche Zeitung.

“I would like the Republican Party to cross this line, move a little further left and place more weight on the center,” Schwarzenegger told the paper. “This would immediately give the party 5 percent more votes without it losing anything elsewhere.”

England said Schwarzenegger is “misspeaking” for millions of Republicans who believe abortion is murder and the life of a child should come before the “mere convenience of a woman.”

“We are outraged that Schwarzenegger would turn his back on two-thirds of Californians — many Democrats included — who voted just four short years ago to protect traditional marriage in this state,” she said. “By embracing gay marriage, Schwarzenegger shows that he is not simply in the ‘center’ on this social issue — he is, actually, far to the left.”

England added, “If Schwarzenegger thinks that the majority of the GOP base will stick with the Republican Party on fiscal issues alone, then he has a lot to learn about the makeup of his own party.”

In the interview, Schwarzenegger was guarded when asked if he had presidential ambitions.

The Austrian-born governor said the debate over whether foreign-born citizens can run is long “overdue,” but he wouldn’t want an amendment created specifically for him.

Schwarzenegger said, however, if such an amendment passed, he would consider running for president.

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