In the referendum – this Saturday and next – Egyptians must accept or reject a basic law that has to be in place before national elections can be held early next year, an event many hope can steer the Arab world's most populous nation out of its turmoil.
At least seven people have died and hundreds have been injured in violence that erupted three weeks ago after Mr Mursi awarded himself sweeping powers to push the charter through a drafting body dominated by Islamists and boycotted by the opposition.
Ahmed Said, a leading member of the opposition National Salvation Front, said pushing through the referendum could provoke more violence as rival voters go to the polls.
"I believe there will be blood and a lot of antagonism, so it is not right to hold a referendum," he said.
Said, who also heads the liberal Free Egyptians Party, described the vote as too much of a risk. Despite a push for a "no" vote from the opposition, the measure is widely expected to pass, given the well-organised Muslim Brotherhood's record of winning elections since the fall of Hosni Mubarak almost two years ago. Many Egyptians, tired of turmoil, may simply fall in line.
However, the divisive referendum risks damaging Mr Mursi's ability to forge a consensus on vital policies to save the economy. It may also fragment an opposition whose present unity may struggle to survive a decisive defeat at the ballot box.
The vote has proved hugely controversial, with supporters of the Islamist Muslim Brotherhood fighting in Cairo and other cities with members of the liberal, secular opposition.
The presidential palace, focus of mass street rallies, is ringed by tanks and huge concrete barricades.