The military's plans
Military leaders have told Arab media that they plan to suspend the constitution, dissolve the parliament and sideline Morsy.
In his place, they would install a mainly civilian interim council until a new constitution can be drafted and a new president elected.
The military's ultimatum was intended to push all factions toward a national consensus, not to seize power through a coup, a spokesman, Col. Ahmed Ali, said Monday in a written statement.
The military appears to be pressuring Morsy to restructure his government to reduce the influence of the Muslim Brotherhood and include opposition members, a source close to highly placed members of Egypt's leadership told CNN.
That restructuring was already happening. Five of Morsy's ministers resigned this week, including Foreign Minister Mohamed Kamel Amr.
And former Prosecutor General Abdel-Meguid Mahmoud will meet Thursday with the Supreme Judicial Council to be officially confirmed in the job.
Mahmoud had originally been installed in the job by Mubarak, shortly before he left. One of the goals during the 2011 revolution had been to oust him, which Morsy did through last November's constitutional declarations.
Mahmoud's return appeared to signify a shrinking of Morsy's power and a tilt toward Mubarak-era officials over Muslim Brotherhood loyalists.
In addition, 30 members of the Shura Council, the upper house of parliament, have resigned, state-run Nile TV reported.
Morsy defends his presidency
Morsy's numerous and adamant supporters point out that he is the legitimate president and say that opponents seeking to depose him are circumventing the democratic process.
The unrest prompted U.S. President Barack Obama to call Morsy on Monday and urge a less rigid stance. "He stressed that democracy is about more than elections," a White House statement said.
He pushed him to form a more inclusive government.
A White House official told CNN that Obama was briefed on the situation in Egypt on Wednesday by his national security staff.
The Obama administration appeared to be giving mixed signals on where it stands. On Tuesday, Obama called on Morsy to hold early elections, a senior administration official said.
"We are saying to him, 'Figure out a way to go for new elections,' " the official said. "That may be the only way that this confrontation can be resolved."
A State Department spokeswoman, however, denied that Obama urged early elections.
Though Muslim Brotherhood leaders have called members to refrain from bloodshed, others have told them to be prepared to die.
And one Islamist group said it would take up arms if Morsy is deposed.
The Egyptian leader's failings
Morsy, a U.S.-educated religious conservative, was elected president in June 2012. But his approval ratings have plummeted.
His government has failed to keep order as the economy has tanked and crime has soared, including open sexual assaults on women in Egypt's streets. Chaos has driven away many tourists and investors.
That has disaffected many among Egypt's poor and middle classes, said Fawaz Gerges, director of the Middle East Center at the London School of Economics.
"The millions of Egyptians who cheered for Morsy are saying he must go," Gerges said.
He called Morsy "incompetent" but said he doubted the military would depose him, adding that that would drive Egypt into an even deeper crisis.