Former New Jersey Gov. Christine Todd Whitman (R) said Sunday that Sarah Palin can't win a nationwide run for the White House, and pointed to the fact that the former Alaska governor left mid-term as an impediment to her support.

Whitman said that Palin could do well in the early states of Iowa and New Hampshire, but pointed out that there will be a lot of competition among Republicans trying to keep President Obama from serving a second term.

"Every congressman and senator right now thinks they can be president," Whitman said on CNN's "Fareed Zakaria GPS".

Whitman said Palin could energize the base of the Republican Party, "but the base isn't big enough."

"I don't think she'll win nationwide," she said. "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."

When asked if she would support Palin as the nominee, Whitman said Palin hadn't yet made her case.

"If she were the Republican candidate she'd have to show me a lot more than I've seen thus far as far as an understanding of the depth and the complexity of the issues that we face," Whitman said. "I mean, I don't know her personally. So I can't comment on that.

"I mean, she was a governor," said Whitman, who served two terms leading New Jersey and then went on to head the Environmental Protection Agency. "But the fact that she left office before even completing her first term is -- that's just not a attitude that I think is necessarily in the best interest of your constituents -- rather what's in your best interests."