Gerges questioned Morsy's ability to continue to lead but said he doubted the military would depose him. Such a move "would plunge Egypt into a greater legal, political and institutional crisis," he said.
The military will want to see the influence of the Muslim Brotherhood reduced in government and in the constitution, Gerges said.
Mubarak had long repressed the Islamic political movement, but it is now the nation's most powerful political force.
Anti-government demonstrators say they have collected 17 million signatures -- 4 million more than the number who voted Morsy into the presidency -- calling for him to go.
The opposition comprises various groups and loose coalitions, some of which are loyal to the ousted Mubarak government, while others want the army to intervene.
AbdulMawgoud Dardery, a former member of parliament and a Muslim Brotherhood representative, told CNN's "Amanpour" that the military could be an "honest broker" in a national dialogue. He said Morsy has reached out to opposition leaders many times, but the opposition "is afraid of democracy."
"It failed in the previous five elections we had in Egypt since the revolution, and they don't want to fail a sixth time," he said. "That's why they're going to street politics."