Protesters, however, say that Suleiman is just more of the same and their chants that Mubarak must go now include Suleiman.
The biggest name to make a play to replace Mubarak is Mohamed ElBaradei, a Nobel laureate and former head of the International Atomic Energy Administration.
El Baradei returned to Egypt last week after the protests started to gain momentum. He speaks fluent English, has worked with American leaders and is popular with progressive intellectual Egyptians, a fact that makes many regular Egyptians suspicious of him.
Many Egyptians find him out of touch and too close to the United States and ironically, Iran. When he arrived in Egypt, he appeared only briefly at the central protests near Tahrir Square but left once police began firing tear gas.
Opposition groups are considering rallying around ElBaradei, partly because he is believed to be a person who would be accepted by the West.
April 6 Group One of the country's most prominent student activists is Israa Abdel-Fattah, a founder of the April 6 Group. Abdel-Fattah was detained by Mubarak in 2008 and has been instrumental in encouraging both students and women to join the protests.
The group takes its name from a 2008 protest when leftists, students and labor unionists backed textile workers in a general strike. The activits were quickly suppressed and many imprisoned. The April 6 Group has also been joined by another youth group, We Are All Khalid Said, named for a student killed by police in Alexandria.
The group of young people has galvanized angry Egyptians, and organized the protests through Facebook and Twitter. April 6 Group has called for a million people to turn out Tuesday in what could be a crucial showdown between demonstrators and Mubarak.
The Muslim Brotherhood
The Brotherhood is a religious movement which seeks to impose Islamic law in Egypt. It is the oldest and largest Isalmist group in the country. It has long been the closest thing to an opposition party in the country, despite being effectively outlawed.
The Brotherhood's immediate influence on the crisis was hurt because it was slow to join secular protesters. Its inability to take action quickly signals to some observers that the party may not be in a real position to govern.
Additionally, the group has no one leader who would make an obvious replacement for Mubarak.
Mubarak was believed to have designated his son Gamal to succeed him as president, in what is often described as a "dynastic succession." Mubarak's American educated second son, Gamal lived in London runs an NGO and had been groomed for years to take over.
That plan, however, seems to have been scrapped in recent days by the protesters.
General Habib Al-Adly
As part of Mubarak's reshuffle, Gen.Habib Al-Adly, the country's hated interior minister was fired. Al-Adly, a longtime member of Mubarak's government, and his ministry have been the focus of smaller protests in Cairo and Alexandria since 2010 when two policemen killed Khalid Said. The officers who allegedly beat Said to death were charged, but have yet to be tried.
Another longtime Mubarak crony who has been the face of public scorn was also axed in the reshuffle. Tycoon Ahmed Ezz, a millionaire accused of taking over the state steel industry, was chairman of the government's budget committee. Ezz a friend of Gamal Mubarak, also resigned from the ruling party over the weekend.