In other words, her appeal is broad. Onstage, Rice sounds alarms about the threat of terrorism while still sounding reasonable. She offers compassion for women in oppressive societies while hard-headedly tying their plight to America’s national security. “I think that societies that treat women badly are dangerous societies,” she insists.

Rice is not the only woman counter-acting the GOP’s narrow image these days. All the unflattering attention paid to Sarah Palin has overshadowed the likes of former eBay (EBAY, Fortune 500) chief Meg Whitman running for governor of California, Maine Senator Olympia Snowe gamely trying to broker a health care deal in Congress, and that other Cheney — Liz — relentlessly making the case for a vigorous “war on terror” to TV and radio audiences.

Rice quashed rumors of a 2008 presidential run and who knows whether she’ll reconsider after she decides to move on from grading papers at Stanford. As Bush’s national security adviser at the launch of the Iraq War, she will never appeal to hardcore Democrats. But to those millions of independents and soft Republicans who pulled Obama over the top in last year’s election — a familiar brand of voter at this Fortune gathering — Rice has allure.