But that opening may not last for long.
"The hope for Egypt is that you have two undemocratic forces that check each other," says Marina Ottoway, a top expert at the Carnegie Endowment on Arab political reform. Recent events have shown that neither Islamists nor the military can take full control of Egypt's fast-moving political transition.
Only last fall, it appeared that the Islamists had the upper hand. The Muslim Brotherhood won 47 percent of the parliamentary seats and, along with the Salafi Nour Party, controlled parliament. But the Brotherhood overplayed its hand: It shut out non-Islamist parties, alienated Christians and urban women, and tried to dominate the writing of a new constitution. It also broke its promise not to run a candidate for president.
Voters soured on the Islamists: In the first round of presidential elections, Morsi received only 25 percent of the vote, slightly more than Shafiq. Those who wanted neither Islamists nor military split their vote between several candidates, permitting Morsi and Shafiq to take the top two slots.
The sliding popularity of the Brotherhood led the military, in turn, to overplay its hand. Just before the runoff, the military carried out a soft coup, dismissing the parliament, and taking control of the constitutional drafting process.
Some observers believed that the SCAF was about to copy the Turkish model - not the current model, where an Islamic party successfully holds power, but the 1997 model, whereby the Turkish military pressured an Islamist prime minister, Necmettin Erbakan, to quit and then banned his party. They expected the SCAF to anoint Shafiq and once more ban the Brotherhood along with Morsi.
Yet, at the critical moment, the military backed off and let Morsi win.
Of course, the battle between Morsi and the military is far from over. The new president intends to challenge the military's dismissal of parliament and its control of the constitution drafting process.
Meantime, two legal suits have been brought to ban the Muslim Brotherhood and its front party, Freedom and Justice; the decisions will be delivered in September. Moreover, compliant Egyptian courts may call for a new presidential election.
Yet, there appear to be some limits on what the SCAF can do.
Egyptian generals appear to have recognized that the 1997 Turkish model no longer applied in the world of 2012. "In 1997," says Ottoway, "the only Islamist the West had experience with was Khamenei. There was not the same focus on democracy in the Middle East; the issue was off the radar screen."
Today, an Egyptian military coup, even one with a "legal" cover, would arouse hostility in Europe - and from both U.S. political parties. Congress would call for a halt in U.S. civilian and military aid to Egypt, which that country desperately needs and its military badly wants.
Equally important, the Egyptian public has become empowered. Anything that smacks of a military coup would push secular and moderate forces back into an alliance with the Islamists, and the military knows this. And not all Egyptian courts are submissive: An administrative court just dismissed a recent decree giving the military the power to arrest civilians.
The public's new empowerment also places some limits on Islamists. Anything that smacks of a Brotherhood plan to monopolize power will create resistance. Morsi knows his party's vote share is declining, and he apparently recognizes that he needs public support against the military pressures. So he is now calling for one female and one Christian vice president and an inclusive cabinet.
Whether the Brotherhood is capable of real change remains to be proved. But secular activists - and U.S. officials - should use this moment of maximum leverage to nudge the Islamists toward pluralism. (Hopefully, the seculars will also begin to organize new grassroots parties, something they've failed at badly in the past.)
And Washington should also urge the military to respect election results and to lessen human-rights violations. So long as the SCAF and the Brothers remain in a standoff, Egypt's democratic forces will have some time to regroup and breathe.