1) As was the case in Iran in 1979, The Philippines in 1986, China in 1989, and a number of lesser event moments (such as Tunisia last month). There is no unified opposition with a plan. You have a broad cross-section of the population that is simply FED UP and this hostility expresses itself in the one thing just about everyone agrees on at this point -- getting rid of Mubarak. After that, no one agrees on anything.
2) The Muslim Brotherhood did pretty well in the one election in which they were allowed to participate a few years ago. They have also been doing their best to "run to the center" during the protests. Critically, they have _not_ tried to claim any credit. They have pronounced themselves willing to participate in any subsequent transition, but are not claiming any mandate. Why? Because they are realists and in it for the long haul. They know they don't have the army , or even a majority of the population. They also know the U.S. (and a lot of other world powers) would oppose their participation in any government. So their goal at the moment is to be part of any "legitimate opposition" as viewed by the Egyptian people so that even those who don't necessarily support them would be willing to have them participate as a legitimate party. They bank on the idea that they could probably again capture between 35%-40% of the vote in an election, making them most likely the single largest block in a post-Mubarak Parliament.
3) What most world powers want is a stable transition in which Mubarak makes an exit and current members of the power elite step in to fill the vacuum with promises of reform and inclusion of some blessable opposition figures, like ElBaradei. Let's call this the "Philippines scenario," as that approximately parallels what happened in the Philippines with the removal of Marco and his replacement by Aquino, another member of the same power elite but open to relatively modest reforms.
There are reasons to believe the Philippines scenario might work. Significantly, the crowds so far have not coalesced around a single leader. True, most of them don't appear to think much of ElBaradei. But no one appears to be clamoring (at this stage) for dismantling Egyptian institutions. Instead, opposition is focused on Mubarak as someone who has hijacked Egypt's government institutions. There is a role model in the Middle East, Turkey, for the idea of a professional officer corp in the Army remaining above politics but ensuring stability by playing Kingmaker and selecting an acceptable (secular) compromise government. There is also the fact that the longer this goes on, the longer a core component of the Egyptian population will simply be looking for stability and return of goods and services to the market.
4) But Egypt also has an extremely large population of unmarried young men who see no future for themselves. While they have not coalesced around any opposition leaders at the moment, they could easily do so. The question is therefore not just what happens to get Mubarak to make an exit. It's what happens over the several months after the Mubarak exit.
This would parallel the Iran scenario. In 1979, the Shah fled and the government in Iran collapsed. For a period of time, the government was up for grabs, with equal likelihood of a secular Marxist or secular Nationalist government modeled on other states in the region. But the religious party was the most organized segment in the mix, and had a charismatic leader in Ayatollah Khomeni. The seizure of the U.S. Embassy and subsequent crisis also provided a significant rallying point for the populace as a whole.
It is possible to imagine a scenario where the Muslim Brotherhood leverages its position as the most organized element of the opposition whether it is allowed to officially participate or not, mobilizing the millions of young men who feel that the current regime offers them no future and that a regime that merely perpetuates the same system is no better. Whether these men are inherently religious or not is less important than the fact that there are millions of them, at just the right age to be highly aggressive, desperately looking for a game changer and feeling disconnected from existing society. Combined with an uprising in Gaza that prompts significant Israeli response and you can recreate the same dynamic that would allow an Islamic religious party to assert control.
A significant moderating factor, however, is control over the Suez Canal. Anything that threatens smooth operation of Suez will bring response not just from the U.S., but from just about every major power. Heck, we could see China or India begin to flex some military muscle. But such a scenario is sufficiently far off that it is hard to predict.
4. That leaves various forms of muddling as the most likely outcome long term. I think there is probably too much pent up anger and frustration -- particularly with the younger population -- for a smooth Philippines scenario. At the same time, I think there is too much secular/conservative opposition to a more revolutionary Iran scenario. This suggests something more like Lebanon. A delicate balance among interests where no one wants to see the state fail, and no one has sufficient support to seize power, but where one or two dominant factions exercise considerable influence. In this scenario, the Muslim Brotherhood ends up playing the role of Hezbollah, but without their own militia. They dominate politics and have a strong influence on policy, but are counterbalanced by other factions. Mind you, Egypt lacks the level of interference in its internal politics by surrounding states the marks Lebanese politics, so its not clear how the various factions emerge and play out. Also, Egypt's population is somewhere in the 80-90 million range and very densely concentrated. This also changes the dynamic in ways that are difficult to predict. Any single faction is likely to be larger than most political parties in other states, and have more in common ethnically and religiously than factions in Lebanon or similar "muddle" states.
Anyway, fun times ahead.