That is the most pressing question of the moment, because as the protests build and show no signs of lessening, it is becoming clearer that its present course is about to be forever altered. What will the new Egypt look like?
There are some who believe that it might actually turn into a more democratic state with increased opportunity and freedom for Egyptians as a whole. But the problem with that particular hope is Egypt's history - it has none which really supports such a state of being. And while we may hope for such an outcome, its chances are slim at best.
While the protests may be popular in nature, at least at the moment, there are some powerful factions lining up to take advantage of the situation to further their agendas. That's realpolitik. They would include other power players as well as organizations such as the Muslim Brotherhood. Suffice it to say, they see unrest such as is happening in the streets of Cairo, as the break they've been trying unsuccessfully to foment for years, decades even.
One of the keys to who will end up holding power is the Egyptian army. Reports have it that infantry carriers and tanks have been seen heading into the streets of Cairo. There are also reports that say some members of the military are joining the protests. If the army supports the current rulers, it will be difficult for the protests to succeed since it is sure to descend into violence and bloodshed at some point. If, however, the army refuses to fire on fellow Egyptians, which is entirely possible (and unlike the Revolutionary Guard's reaction to the Iranian protests), it is a matter of time before the government falls.
The position of the US, as with all other countries, is one in which it is forced to look on and hope for the best. President Obama has spoken with Egyptian President Hosni Mubarak and advised him to consider the demands of the protesters and eschew violence to put down the protests. There have been reported deaths among the protesters, but not any incidents of wholesale violence yet. Mubarak asked his entire cabinet to resign which some took as a sign he was willing to consider the message of the protests. But then he appointed long time confidant and intelligence chief Omar Suleiman as his Vice President. It is a move that has dampened speculation that Mubarak is ready to consider the demands of protesters and is, instead, digging in with an eye on holding on to his power.
The ramifications of a change in government in Egypt are huge. Like it or not, they've been an ally of the United States since the days when Anwar Sadat made the bold decision not to engage Israel militarily anymore and to work toward a stable peace. It is one of those conundrums which foreign policy causes nations to face constantly - staying with an ally that doesn't have a great human rights record. Pragmatically, even with a less than stellar human rights record, the best interests of the US are served by engaging and allying with that country. The downside of that is if the government then changes, that position is hard to justfy to those who form the new government.
Additionally, it truly depends on what emerges as the government that will be the final determiner of whether or not it will be willing to engage with the US. If it is a secular and democratic government, diplomacy may be able to mend the appropriate fences and aid to smooth the ruffled feelings. If it is another strongman, then the US is faced with deciding whether or not it is in its best interests to engage the government formed. And it is possible the strongman will shop his allegance to other powers, such as China. It is also possible that a new strongman may be so oppressive that it is impossible to condone a relationship regardless of the US's best interests being served. Finally, it is possible that a theocracy may emerge as it did in Iran. Muslim nationalism is at an all time high and various factions throughout the Middle East are working toward the Islamification of all governments within the region. Establishing a working relationship with that sort of a government would be very difficult.
The Egyptian situation is a very fluid one and may break toward a conclusion at anytime. And, as we're seeing elsewhere, it isn't the only country in which such discontent is surfacing with a possiblity of forcing change. The Middle East has always been called a "tinder box", but never before, other than attacks on Israel, has the Arab world been faced with its own "tinder" being the focus of the fire.