Egypt is holding its breath for mass demonstrations to mark the first anniversary of President Mohamed Morsi's election on Sunday, amid speculation the army might intervene in the event of large-scale civil unrest.

Opposition activists claim an unverifiable 15 million Egyptians have signed a petition demanding Morsi's removal, and expect a significant proportion of that number to take to the streets on 30 June. There have already been outbreaks of fighting in two cities, where Morsi's still-sizeable support base has launched counter-protests. As a result, many opposition actors hope the army, who deployed armoured vehicles on Cairo's streets on Wednesday, will be forced to intervene and facilitate a transition of power.

A senior military source told the Guardian on Thursday that the army did not want to intervene. But they stated that if Sunday's protests were as widespread and prolonged as those that drove Egypt's 2011 uprising, and if serious fighting broke out between Morsi's supporters and his opponents, then the army may regard the protests as a more legitimate representation of the people's will than the elections that brought Morsi to office a year ago – and would step in to facilitate a transition of power to a technocratic caretaker government.

The eventual scale of the protests nevertheless remains uncertain, and could yet prove highly exaggerated. But some of Morsi's opponents are convinced 30 June will be as pivotal as the 2011 uprising that toppled Hosni Mubarak.

"It's a second revolution," claimed Ahmed Said, a leader of the National Salvation Front (NSF), the secular opposition's largest coalition. "The semi-final was played on 25 January 2011. This is the final. I don't know how long it will take, but Morsi's going to go – and Egypt will never be the same after the 30th."

But protesters may have underestimated the size of Morsi's support, as well as the lethargy of Egypt's silent majority – many of whom may have been won over by Morsi's earthy speech to the nation on Wednesday night. Though recent polls suggested his popularity had halved since last autumn, his core following remains strong, and can mobilise just as easily as his opponents. At least 100,000 Islamists gathered in east Cairo last Friday to recognise Morsi's democratic legitimacy – and will do so again this week. They suggest his critics put their energy into campaigning for parliamentary elections, which are expected to be held in the next six months.

"Democracy all over the world works in the same way," said one of them, Sabry Roushdy, a teacher from Kafr-el-Sheikh, northern Egypt. "You come by the ballot box, and you go by the ballot box. It's not right that a section of society should bring him down just because they don't think he is good for the country."

Morsi himself refused to consider standing down during his two-and-a-half-hour speech on Wednesday. He apologised for some of his mistakes, and offered to let opponents help amend parts of Egypt's divisive new constitution. But in the main he focused on shoring up his own support – and blamed attempts to unseat him on "enemies of Egypt" bent on undermining democracy.

With all factions unwilling to make compromises acceptable to their opponents, neutral observers fear a violent outcome. "Egyptians are living in their own bubbles," said Nathan Brown, a professor of Middle Eastern politics at George Washington University. "The number of actors who think they speak for the entire Egyptian people is a little bit troubling. The presidency thinks it has been elected by the entire Egyptian people. The army think they are one hand with the people. The opposition think they are the entire society."

Brown said that "in almost any other country", such profound polarisation might lead to civil war. He ruled out such an outcome in Egypt, where the various factions have no organised militias, but nevertheless anticipated some kind of breakdown in political and civil order.

Clashes have already broken out between Islamists and their opponents in some northern cities, with two killed and more than 200 injured in Mansoura and Tanta. Many Egyptians expect even worse on Sunday, and have resorted to panic-buying food and petrol, leading to snaking queues at most gas stations, sparse shelves at many shops – and a shortage of cash at some banks.

In a sign of international concern at developments, the US ambassador to Egypt, Anne Patterson, spent much of last week trying to convince opposition leaders to rein in their demands.

Some want early presidential elections to end the impasse – but others demand Morsi's immediate departure. They want the army to help replace him with a neutral, technocratic cabinet who would oversee the re-writing of Egypt's new constitution before organising new polls.

It was the creation of the Islamist-slanted constitution last November that first sowed the seeds of major dissent. For his opponents, Morsi's unilateral decision to fast-track its completion – despite major secular objections – was the act of a dictator. It showed that while he may have been elected democratically, he is unconcerned about the wider democratic values on which successful democracy depends. For some, it also indicated Morsi was unwilling to build the political consensus that many of those who tentatively voted for him expected him to seek.

"Yes, the opposition must share their portion of the blame," said Yasser el-Shimy, Egypt analyst for the Crisis Group. "But President Morsi should have done more to reach out. The most detrimental act of Morsi's tenure so far has been that he has not assiduously built consensus and reconciliation as much as he should have."

Morsi's decision to award key government positions to his allies rather than his opponents has angered the latter camp, while he has been blamed for the repression of dozens of journalists and activists such as Bassem Youssef and Alaa Abdel Fattah. Rights campaigners also lament his failure to reform the police, whose brutality helped spark the 2011 uprising, and continues unabated. Most notably, following the deaths of more than 40 protesters in Port Said during gun battles with the police in January, Morsi chose to praise police actions, rather than investigate them. "For me, that was pretty much the end," said Heba Morayef, Egypt director for Human Rights Watch. "Those last shreds of optimism that I had were lost finally and conclusively in January, with his response to the Port Said crisis."

Morsi's allies maintain that his attempts to reform Egypt have been hampered by Mubarak-era holdovers. But that is scant consolation for Egypt's poorest, many of whom blame his government's incompetence for a marked fall in living standards. Egypt's economy is on the brink, leading to ballooning food prices, and widespread fuel shortages. "He's ruining the country," said Yasser Abdel Samir, a Mansoura resident who had spent hours queuing for petrol. "Look at this petrol queue. That's because of him. There's no water. There's no electricity. Salaries are low. Food prices are high. He's going down on the 30th."

But such an outcome is unlikely without the intervention of the military. Analysts emphasise that the army has little desire to involve itself after its mixed attempt at interim government following the fall of Mubarak. "The military will only intervene as a last measure – to prevent the collapse of the state itself," said Shimy. "They know that they will be trying to catch a falling knife if they try to take over."

Shadi Hamid, director of research at the Brookings Doha Center, argued that Morsi and his political opponents might yet agree to a compromise before such an intervention was necessary.

"I think you'll see very large protests, clashes here and there, and a certain amount of deaths around the country," said Hamid. "But the fundamental balance of power will remain. Morsi will stay, and we'll have an effective stalemate. Perhaps the reality of that stalemate, when it dawns on people that Morsi hasn't left power, will force both sides to finally get serious about sitting down and making concessions."

But for now Egypt remains dangerously split, with many past the point of assigning any legitimacy to their opponents' points of view. "Are you Brotherhood," asked one opposition activist of passersby in Mansoura this week, "or are you Egyptian?"