Morsi's opponents calculate they can push him to go through the sheer number of people they bring into the streets Sunday—building on widespread discontent with his running of the country—plus the added weight of the army's backing.
After that, they believe that the Islamists have misruled so badly that a new election would yield a different result.
Morsi's backers, in turn, say the mainly liberal and secular political opposition is fomenting a coup to remove an elected leader because they can't compete at the ballot box.
Central to whatever happens on June 30—the anniversary of Morsi's inauguration—is the stance of the military.
Last Sunday, Egypt's army chief gave the president and the opposition a week to reach an understanding to prevent bloodshed and warned it would intervene to stop the nation from entering a "dark tunnel."
Gen. Abdel-Fattah el-Sissi also gave a thinly veiled warning to Morsi's backers that the military will step in if the protesters are attacked during the planned protests, as some hard-liners have threatened.
In the days since, there's been no movement toward a resolution. Morsi has given no signs of making any concessions. He invited all sides to a meeting Wednesday, when he plans a national address. The opposition in turn rejects talks, saying they come "extremely late." It is boycotting the meeting, saying it is not serious, and will only join a dialogue if el-Sissi convenes it—a sign of how it sees him as the only reliable arbiter.
"There is just no time left. It is too late and anything the president tries to do now will in reality be an attempt to discourage people from coming out on Sunday. We have no confidence in the president," said Khaled Dawoud, the spokesman for the National Salvation Front, the main opposition grouping.
In his comments, el-Sissi said the two sides must reach a "genuine" reconciliation, seeming to acknowledge the opposition's argument that Morsi's past calls for dialogue were empty gestures.
The opposition has laid out a post-Morsi road map that would have the chief justice of the Supreme Constitutional Court step in as interim president, a non-partisan figure as prime minister heading a small Cabinet of technocrats, an expert panel to amend the Islamist-backed constitution and new presidential elections six months later.
How to get to that point is less clear.
If the protesters are attacked by hardcore Morsi supporters and the army sides with the protesters, it would add significant pressure on the president. At the least, the army is likely to deploy to protect vital institutions like the state TV, parliament, the Cabinet, and the media complex that houses a multitude of TV networks, some critical of Morsi.
The opposition seems confident it can have army intervention without the generals actually taking power like they did after Mubarak's fall.
"Unlike last time in 2011, the military will not intervene to rule but to protect a people against a regime that is no longer wanted," said Ammar Ali Hassan, a prominent analyst and author. "There seems to be agreement by the military over the road map charted by the protest movement."
Morsi's office has depicted his comments as a sign of support for the president's "legitimacy."
Presidential spokesman Omar Amer underlined to reporters that Morsi is supreme commander of the armed forces and said "there is complete agreement and coordination" between him and el-Sissi.
Another Morsi spokesman, Ihab Fahmy, said el-Sissi's comments were made in coordination with the presidency and "were intended to defuse tension."
But some of Morsi's Islamist backers saw el-Sissi's statement as a slap and were furious.
"The comments made by Abdel-Fattah el-Sissi ... are extremely reckless, a blatant and public aggression and a prelude to a coup that is unacceptable to anyone with dignity and self-respect," Hazem Abu Ismail, an ultraconservative Salafi who backs Morsi, wrote on his Facebook page.
An opinion piece posted on Tuesday on the website of the Freedom and Justice Party, the Brotherhood's political arm, berated the opposition for wishing for a military coup.
"You are urging the army, as represented by Gen. el-Sissi, to stage a coup against legitimacy and to return to power. You have forgotten that you were the first to chant for the fall of military rule," Said el-Ghareeb wrote in the article.
Questions remain whether the military has enough motive to jump back into the political fray.
The military has secured its special status in the new constitution as a self-ruled institution with little outside oversight over its finances or massive business interests.
It also is likely loath to expose itself to the harsh criticism and blow to its prestige it suffered during the nearly 17 months after Mubarak's fall when the generals directly held the reins of power. Chants of "down with military rule" and personal insults directed at the army's top brass were common amid protests over its perceived mishandling of the nation's transition to democratic rule and over its human rights record.
Still, perceptions of the armed forces have dramatically changed in the year since Morsi took office.
The U.S. and British-trained el-Sissi was named as defense minister and army chief by Morsi in August after the newly inaugurated president forced out the Mubarak-era head of the military, Field Marshal Hussein Tantawi.
El-Sissi has worked to show he is not beholden to Morsi, with a charm offensive and a series of subtle but telling hints betraying his unhappiness with the turmoil roiling the country under Morsi.
On several occasions, he sought to reassure Egyptians the military will spring to their defense if needed and at times appeared to do things just to spite the president and ingratiate himself to the opposition.
For example, he sent a military aircraft to airlift to hospital a TV show host who is a harsh Morsi critic when involved in a road accident in southern Egypt. Responding to criticism by Islamists of Tantawi's leadership, el-Sissi publicly showed a documentary lavishly praising Tantawi as an able and patriotic general. He also remained silent on a series of leaks to the media by unnamed military officials on the army's growing unhappiness with Morsi and his backers.
The military may also have other reasons to throw its weight behind those seeking an end to Morsi's rule—concerns over the security implications of rising Islamic extremists.
El-Sissi has cited sectarian and internal strife as well as the collapse of state institutions as justification for intervention by the military.
In the past year, hard-line Islamists have enjoyed a significant measure of tacit support from the Morsi administration. Militants, for example, have carved territory they virtually control in the strategic Sinai Peninsula bordering Gaza and Israel.
Militants also received implicit administration approval to travel to Syria and wage jihad, or holy struggle, on the side of the rebels, raising the prospect of their eventual return with a more radical ideology and enhanced combat capabilities.
The military is also known to be wary of Morsi's close ties to Hamas, the Palestinian chapter of his Muslim Brotherhood which it views as a threat to Egypt's security. Sectarian hate speech by Morsi allies has swelled, and on Sunday a mob lynched four Shiite men in what was seen as a dangerous and unprecedented development.
Hendawi is the AP's chief of bureau in Cairo since 2010. He has covered the Middle East for the AP since 1995.