President Mohammed Morsi, from the fundamentalist Muslim Brotherhood, rammed the draft through an assembly and rushed it to a vote the next two Saturdays.
The vote on the draft has sharpened the polarization in Egypt between Islamists and liberals.
Liberal and secular activists charge that the draft opens the door to rights abuses and Islamist domination.
The National Salvation Front of opposition groups, is organizing a demonstration Friday, after deciding to call on followers to vote "no."
The Coalition of Islamist Forces is describing a vote in favour of the draft as "yes" for Islam and is staging its own rally.
Egyptians abroad are voting for a third day.