WASHINGTON (CNN) -- A senior political advisor to Sen. Hillary Clinton shot back at Vice President Cheney Tuesday, hours after Cheney said the New York Democrat would not be a good president and predicted she would fail in her bid for the White House.

Clinton, who just won a second six-year term to the Senate in November, announced this past weekend she would explore a campaign for the Democratic presidential nomination.

Cheney provided his candid assessment of Clinton during a wide ranging interview with CNN's Wolf Blitzer. When asked by Blitzer why he didn't think Clinton would make a good president, Cheney cited political differences.

"I don't agree with her philosophically and from a policy standpoint," the vice president said.

Howard Wolfson, a Clinton advisor, in turn criticized Cheney for the Bush administration's assertion that there were weapons of mass destruction in Iraq -- a key premise to invading the country. So far, no such weapons have been found.

"Didn't Dick Cheney tell us he knew where the weapons of mass destruction were? His track record on predictions isn't very good," Wolfson said.