Sarah Palin is going to have to work for the vote of one former Republican governor.

Christie Todd Whitman (R-NJ) told CNN's Fareed Zakaria Sunday that Palin might win the Republican nomination but lacked the "depth" needed to be president.

"I don't think she'll win nationwide," Whitman said. "The base isn't big enough. And Republicans should have learned that. In this last presidential election, John McCain's election, you had over 2 million self-identified born-again Christian Republicans, pro-life Republicans who voted in that election and then voted in George Bush's re-election. So we got them all out, the base all came out, and we still got our heads handed to us."

"You've got to start competing for the center. And so far, I haven't seen a lot of outreach on the part of Sarah Palin for that. She's more concentrated on that base and energizing them, which is fine, but it's not going to win you a general election."

"Would you support her?" Zakaria asked.

"If she were the Republican candidate? She would have to show me a lot more than I’ve seen thus far, as far as an understanding of the the depth and the complexity of the issues that we face," Whitman replied.

"The fact that she left office before even completing her first term is -- that's just not an attitude that I think is necessarily in the best interest of your constituents, rather what's in your best interests," she observed.

Whitman also warned Republicans against overreaching after they take control of the House in January.

"I think the biggest mistake Republicans can make is just standing up and saying no to everything," she said.

"I guess they'll have to go through the drill of, 'we're going to repeal the health care,' but most Americans don't want the health care reform repealed. They want it improved, changed."

"This idea that compromise is somehow defeat, actually is the antithesis of the way this country was founded," she added.