The group retains much grass-roots support in rural areas of Egypt, where it has long provided free social services. A recent Zogby poll contends that the country is pretty evenly divided between Brotherhood supporters and opponents.
What's more certain is that - despite the apparent defeat of political Islam by the July 3 coup - the Brotherhood's place in Egyptian politics remains unsettled. No one knows if it can be reintegrated into some form of democracy - or what will happen if it's not.
"The military understands that the Brotherhood cannot be forced out of existence by force," says Ashraf El Sherif, an expert on Islamist movements at the American University of Cairo. "Sooner or later the military will make a deal. The question is the terms."
The generals, says Sherif, want the Brotherhood to accept the role of junior partner in the system, giving up any effort to play a dominant role. The Brotherhood wants its organization restored and its prisoners released. It also seeks some kind of referendum that tests popular opinion on the army's coup and post-coup moves.
Intermediaries have reportedly sought to find some area of compromise between military and Brotherhood. So far, there is no sign of movement. Yet the military and Brotherhood have a long history of doing secret deals, during the years when the Brotherhood was banned, and even when Morsi came to power.
At present, the military's take on the Brotherhood, constantly echoed in the media, is totally black and white. It thoroughly demonizes the group, depicting it as a violent sponsor of jihadi terrorists in Sinai. (U.S. and Egyptian terrorism experts I've interviewed reject this direct linkage.) Morsi is being tried on a murder charge.
Needless to say, Brotherhood lawyer Tosson has a different perspective. He concedes that Morsi made big mistakes - for example, in trying to undermine the judiciary and - for one key period - declaring himself above the constitution. These moves convinced many Egyptian liberals that Morsi had a dictatorial bent.
Tosson insists the question is one of political legitimacy, which belongs to Morsi because he was elected. "I visited France when Sarkozy was president," he says, "and his popularity was sinking. If people went to the streets and asked the president to resign, would his government have accepted that?"
There is also a huge element of self-denial in his and the Brotherhood's insistence that the numbers marching in massive anti-Morsi demonstrations of June 30 were only a small fraction the millions claimed by organizers and observers. The Brotherhood's paranoia and insularity come through when Tosson insists that this false information comes from media "controlled by the Zionists all over the world, which convince you that Egypt was heading for a religious government.
"This was not true," he insists.
(Paranoia is not the exclusive terrain of the Brothers; the military sometimes claims the original Tahrir Square revolt was an American plot.)
With the Brotherhood and the military both playing for time, Egypt's politics and economy are stuck in the middle. "As time moves on," Sherif says, "the cost of reconciliation gets higher."
Brotherhood demonstrators have suffered hundreds of casualties at the hands of security services, which enrages young followers of the movement. This holds the potential for more violence. Meantime, egged on by state media, large segments of the public are also getting angrier with the Brotherhood, blaming it for their economic woes.
"The Brotherhood feels it can delegitimize the system and cause trouble," says Sherif, thereby causing instability that undercuts tourism and investment. On the other hand, the military is betting it can squeeze the Brotherhood to accept its terms.
Ex-parliamentarian Anwar El-Sadat, nephew of the former president, has tried to start behind-the-scenes negotiations to find a compromise. "We all understand we can't live without them, but the timing is important - how to do it when the people are angry [at the Brotherhood]." So far, neither military nor Brothers seem ready.
Nor have Brotherhood leaders decided whether their party will participate, directly or indirectly in elections, although experts think they could still win many seats.
Some leading Egyptians think the country can muddle through whether or not the Brotherhood comes around.
"This is not the time for political Islam," says Egypt's elegant diplomat Amr Moussa, former Arab League head and chair of the 50-person committee that just drafted a constitution.
"One year of Muslim Brotherhood rule showed it was bad rule," he says. "It was not [only] a question of political Islam. It was the way the Muslim Brotherhood and their friends in the region exercised it. That is over."
Now, says Moussa, Egypt is embarking on a new round of elections and the Brotherhood's front Freedom and Justice Party should be able to run if it "stops violence and provocations, and trying to paralyze society. Otherwise society itself will reject them."
In that case, he added, "We will live with it, and they will just be a pain in the neck."