The Egyptian military has given President Mohammed Morsi until Wednesday to reach a deal with opposition protesters, and as the deadline fast approaches there is still no solution in sight. Indeed, demonstrators demanding Morsi's ouster launched fresh mass rallies on Tuesday, while Morsi's fellow Islamists in the Muslim Brotherhood urged his backers to stand firm against a possible coup.

What will happen if the military makes good on its threat to intervene?

If Morsi does not come up with a plan to make peace with his rivals, military sources say the generals will begin implementing their own power-sharing roadmap, according to Yasmine Saleh and Asma Alsharif at Reuters.

The plan, which is still nebulous, calls for suspending the constitution — written and pushed through by Morsi's party — and dissolving the Muslim Brotherhood–dominated parliament, according to Reuters. The army would reportedly install an experienced and predominantly civilian interim council to run the country for the next few months, until an amended constitution can be drawn up.

Next would come a new presidential election, followed by the vote for a new parliament — although there was no word on what the military planned to do with Morsi "if he refused to go quietly," Reuters says.

Analysts largely agree that the military is not eager to take power itself. The generals seized the reins after Egypt's Arab Spring revolution forced out longtime leader Hosni Mubarak in 2011, and wound up becoming the target of angry crowds. Jeff Martini at Foreign Affairs says that the military is "still licking its wounds" after that experience, and would be better off pulling together a real caretaker government, which means getting at least some Islamist groups on board.

An intervention absent Islamist support would risk an Algeria-like scenario, in which the military's overturning of an Islamist electoral victory led to a civil war that embroiled the country throughout the 1990s. To mitigate against the possibility of a violent response, the military could try to coax the Muslim Brotherhood to the bargaining table with the opposition. Failing that, it could try reach out to Islamists from outside the Muslim Brotherhood, such as the Salafists, or breakaway groups, such as the Strong Egypt and Center parties. [Foreign Affairs]

However, there's also the very real possibility that a coup could spark another round of protests, this time led by the Muslim Brotherhood. That could push stability further out of reach, says The New York Times:

Faced with fuel shortages, dwindling hard currency reserves and worries about its wheat supplies, Egypt urgently needs a government stable and credible enough to manage difficult and disruptive economic reforms. A move by the military to force the Brotherhood from power, despite its electoral victories, could set off an Islamist backlash in the streets that would make stability and economic growth even more elusive. [The New York Times]

There is also the uncomfortable fact that the military would be involved in dismantling a democratically elected government. Ariel Ben Solomon at The Jerusalem Post notes that the country may be on the verge of repeating history — and not in a good sense:

If Abdel Fattah el-Sisi — defense minister and commander in chief of the Egyptian Armed Forces — decides to take full power, it would not be the first time that Egypt experienced a coup.

In 1952, Gamal Abdel Nasser, a strong nationalist leader of the Free Officers Movement, overthrew King Farouk and then moved to abolish the constitutional monarchy, leading to a series of dictators that came from the army as well. [Jerusalem Post]