The new constitution was approved in a rushed, all-night session without the participation of liberals and Christians.
Anger at Mr Morsi even spilled over into a mosque. In his sermon, the preacher compared Mr Morsi to Islam's Prophet Mohammed, saying the prophet had enjoyed vast powers as leader, giving a precedent for the same to happen now.
"No to tyranny!" congregants chanted, interrupting the cleric. Mr Morsi took to the podium and told the worshippers that he, too, objected to the language of the sheik and that one-man rule contradicts Islam.
The crowd appeared comparable in size to the 200,000 anti-Morsi protesters who thronged Tahrir on Tuesday.
In contrast to the largely leaderless uprising by youth activists against Hosni Mubarak last year, a more cohesive leadership has started to emerge in the new campaign against Mr Morsi, Egypt's first freely elected president.
It is made up of a number of prominent liberal, secular and moderate Islamist politicians, notably reform advocate Mohamed El Baradei.
"We are determined to continue with all peaceful means, whatever it takes to defend our legitimate rights," Mr El Baradei told the Tahrir crowd.
His ally, senior opposition leader Hamdeen Sabbahi, vowed protests would go on until "we topple the constitution".
"The revolution is back. We shall be victorious," said Mr Sabbahi, a liberal politician who came in a surprisingly close third in last summer's presidential election.
The protests were sparked by the president's decrees a week ago granting himself sweeping powers and neutralising the judiciary.
The edicts tapped into a feeling among many Egyptians that Mr Morsi and the Muslim Brotherhood, from which he hails, are using their election victories to monopolise power and set up a new one-party state.
But the sudden adoption of a draft constitution by the Islamist-dominated assembly tasked with producing the document throws the confrontation into a new phase.
The draft must now be put to a nationwide referendum for public approval, likely to be held in mid-December.
Mr Morsi is expected to announce the date today.