President Mursi has rescinded much of his decree claiming total power right now. But he could accomplish much the same thing after the Constitution is confirmed and perhaps by forcing reinstatement of the parliament whose election was declared invalid by a court. At any rate, Mursi's concession has not quieted the demonstrations--another sign that concessions in the Middle East don't bring agreements--and so this crisis isn't going away.
Now Mursi has given the army the power to arrest civilians but does it want to do so? The army doesn’t want to be hated, shoot down people, and set off a civil war in which it has to round up hundreds of thousands of people and launch scores of operations each day. True, the police are obedient and will act against these demonstrations just as it formerly tried to repress the anti-Mubarak demonstrations. But the police alone aren’t sufficient.
Then, the opposition will be told: you’ve lost, accept it; you have no choice. And besides, we are acting legally under this Constitution that the people accepted.