Forget the legalities, it's about process and symbolism, and Morsi has royally fucked up:
The answer no longer lies in a draft constitution that very few of the demonstrators, on either side, are likely to have read. Egyptians along with the citizens of a great many other places have learned what is on paper is only a part of the constitution. The other, most important, part lies in the institutions that give the constitutional language presence in everyday life. To some degree this means the habits and choices of low level officials and to some degree it means the courts. And the simple and sad reality for the Brotherhood is that a great many Egyptians distrust, dislike, or fear them and worry that, having come to control the legislature and central executive, they plan to take over the courts as well as staff many of the lower levels of the government.
President Morsi has been unable to allay this distrust, fear, and dislike and over the last week he and his allies have, through words and actions, intensified it. This may be unfair and its results may be tragic, but it remains a profoundly political issue with which he and any Egyptian politicians who aspire to lead the country will ultimately have to deal.
Morsi and his advisors also seem to believe that they can use any stratagem, as long as it remains formally valid, to accomplish their substantive ends. In this they are, regrettably, all too like Egyptian governments of the last 60 years. One of Morsi's advisors admitted that, having been unable to remove former Public Prosecutor Abdel Meguid Mahmoud by ordinary means, Morsi simply changed the constitution to make it feasible (this was supposed to be one of the sections of the declaration that rendered it palatable to the public). Equally remarkably, the MB members of the Constituent Assembly even overrode the advice of the assembly chair and ally, Hosam al-Gheriani, to deny former leaders of Hosni Mubarak's National Democratic Party political rights for a decade and to grant members of the government's prosecutorial staff judicial immunity. Al-Gheriani was reduced to leaving the dais of the assembly in protest against these provisions. He described the one as political vengeance and the other as an assault on the rights of citizens.
There are probably very few sections of Egyptian society that the Brotherhood and its allies in the Salafi movements have not antagonized.
The other important thing is that the anti-Morsi sentiment out there is not directed by the opposition leaders who are appearing on TV. It's a popular movement of anger by people who feel they were slapped in the face — twice — by the Morsi administration rushed, unthinking actions and the discourse of their supporters.
Goldberg also has some fine words about Obama policy on this.