That statement, along with a call by Christie to cut Medicare benefits, was captured on tapes from an undisclosed trip that Christie made to Colorado on June 28. It was published online by the left-leaning magazine Mother Jones.
The event, a fund-raising and strategy session at which the governor was a keynote speaker, was sponsored by the controversial conservative financiers David and Charles Koch.
In an interview Wednesday, Oliver called the governor's statements about her "outright lies" and said, "At no time did I ever, ever pick up the telephone, call Gov. Christie and ask him to 'save my leadership.' "
She said the governor was engaged in a "chest-thumping bravado entertainment session" for Republican donors.
"That to me is a characterization of someone that is not fit to lead the state. . . . I think it's disgraceful," Oliver said.
A spokesman for Christie said the governor stood by his story.
Asked about a deal with Oliver at a news conference in Atlantic City, Christie described it as "another example of the way we've found to work together."
The trip to Colorado was not on Christie's public schedule. The state Republican Committee paid for his flight.
Such travels out of state are only likely to increase because the Republican Governors Association announced Wednesday that Christie had been elected vice chairman of the organization, boosting his fund-raising and party leadership responsibilities.
In June, Christie was introduced at the Ritz-Carlton Beaver Creek Resort by David Koch (pronounced Coke), who with his brother owns the second-largest privately held company in the country, Koch Industries, an energy and chemical conglomerate.