Updated

On the eve of Wednesday's closed door meeting with President Obama, Senator McCain warned that the White House needs to make sure demonstrators know they will never achieve their goals if radical Islamic extremists are allowed to "hijack" the government."

"ElBaradei is not a friend of the United States," McCain said, cautioning that the emerging leader "could be a figurehead for the Muslim Brotherhood, since he has no real following in Egypt, he's lived most of his life outside of Egypt."

The Arizona senator will head to the White House Wednesday afternoon for a private meeting with the president. A senior White House official says the president is "eager" to see McCain and that "they hope to discuss a number of important issues," Fox News' Mike Emanuel reports.

A McCain aide tells Fox News that the president extended the invitation with no specific agenda, but noted that free trade, the earmark ban, immigration, and Egypt are likely to come up.

And if McCain's criticism of the Muslim Brotherhood in an appearance on "Hannity" is any indication, the White House's approach to that organization could be a topic of discussion. "I hope he addresses that issue and does as quickly as possible," McCain said, blasting the Muslim Brotherhood as "by any definition, a radical Islamic organization, although they may be portraying themselves as somewhat different."

The lawmaker stressed that the United States will have to rely on the Egyptian military to ensure a stable transition to a new government."I believe that success or failure -- Egypt reverting or moving to a radical position -- is directly related to how the army is able to control things and make sure they have free, open, fair elections," he said.

Calling the Egyptian military "an institution that is respected all over Egypt," McCain put hope in their "close relations with the United States, particularly the United States military."

The military's weekend vow not to use force against the Egyptians, "acknowledging the legitimate rights of the people," appeared to encourage the massive turnout at the pro-democracy rallies Monday. Still, there is some debate among analysts regarding how much faith the White House should put in the Egyptian military during this period of transition.

"This is...one of the most tense, difficult, dangerous times in our history," McCain said, adding that the president should draw a contrast between the goals of the protestors and radicalized government. "I think he has to make that message very loud and very clear."

Mike Emanuel and April Girouard contributed to this report