Former Assemblyman Howard Kaloogian, in contrast, proclaimed himself a true conservative - provoking the most approving nods as he addressed the convention-goers, who traditionally are among the party's most right-leaning members.
"We cannot run from our base," he said during the lunchtime forum with his three rivals.
Kaloogian also said he believed that many women are "coerced into abortion."
He tried to boost his Senate bid by headlining a late-morning rally to protest resurrected legislation to give some illegal immigrants driver's licenses. Schwarzenegger persuaded lawmakers to repeal a previous law after he won office, but has said he would sign a new bill if it contained adequate security measures.
Hundreds of people gathered for the rally, some holding signs that read "No terrorist driver's license," and included a blow-up of a California driver's license with Osama bin Laden's photo on it.