Giuliani said that the Obama administration had not talked with oil industry experts about how to stop the leaking well.

"Two days ago I had dinner in Houston, with several people who are top people in the industry. [The Obama administration] never reached out. Never, never asked, 'Gee, has Shell done this before? Has Exxon done this before?' If your father or mother was sick, you would go get a second opinion from an expert doctor. Not from an academician which is what he did. Go ask the question. Anybody does remediation before or better than BP? Bring them in. Make them your eyes and ears. Have them watching everything. Maybe they could have gotten the estimate right of the amount of oil coming out," said Giuliani.

"And people in the industry believe that [Obama] hasn't talked to the industry because they are bad guys," Giuliani continued.

Brzezinski accused the former mayor of taking "cheap shots" because he had "an axe to grind" with the Obama administration.

A viewer wrote in to the show Monday complaining about Brzezinski's criticism of Giuliani. "I think Mika should be given a small desktop lectern like the one Robert Gibbs uses for his daily White House briefing. Clearly, she deserves some recognition from the executive office for the unending enthusiasm to regurgitate every talking point they send her," wrote one viewer from North Carolina named Gary.

Brzezinski defended herself. "I'm glad that there is someone on the set asking questions when people come and vomit out complete baseless lies on our set," she quipped.