The Islamist leader won a 57% yes vote for the constitution in the first round of a referendum at the weekend, according to state media, a small margin that is likely to embolden the opposition.
The second round, due on Saturday, is expected to give another "yes" as voting will be in districts seen as even more sympathetic towards Islamists, which would mean the constitution being approved.
President Mohamed Mursi and his backers say the document is vital to moving Egypt's democratic transition forward. Opponents say it is too Islamist and ignores the rights of women and minorities, including Christians.
The opposition National Salvation Front urged the referendum organisers to investigate what it said were widespread voting violations. Yesterday, it called for protests across Egypt and urged organisers to consider re-running the first round.
Senior opposition politician Mohamed ElBaradei used his Twitter account to call for "cancelling the notorious referendum and entering dialogue to mend the rift".
The closeness of the vote and a low turnout of one-third of those eligible will give Mr Mursi little comfort as he bids to assemble support for economic reforms to reduce Egypt's budget deficit.
Simon Kitchen, a strategist at Egyptian investment bank EFG-Hermes, said much would depend on whether he took the result as "an endorsement of his policies ... or does he recognise he may need to spend time building consensus ahead of major policy changes?"
He added: "I think he will continue to push ahead on reforming taxes and subsidies because Egypt has little choice but to make such reforms."
However, some analysts said they remained concerned by voting patterns that seemed to show a deepening sectarian divide, notably in Alexandria, Egypt's second city, where tensions between Christians and conservative Muslims run high.
Mustapha Kamal al Sayyid, a professor of political science at Cairo University, said: "This percentage will strengthen the hand of the National Salvation Front and the leaders of this Front have declared they are going to continue this fight to discredit the constitution."
If the constitution passes, elections can take place early next year.
Economists said the parliamentary election timetable could affect the timing of reforms, encouraging Mr Mursi to delay tougher measures.
To rein in a large budget deficit, the Government needs to raise revenues with tax rises and to cut back on subsidies on fuel, one of the biggest drains on funds.
Both will be unpopular, and the Government has outlined plans to target fuel subsidies more directly at the poor, in a nation where everyone has become used to cheap energy.
Uncertainty over reform has already forced the delay of a £2.9 billion loan from the International Monetary Fund.
The build-up to the first round vote was marred by violence.
Demonstrations erupted when Mr Mursi awarded himself extra powers and fast-tracked the constitution through an assembly dominated by Islamist allies and boycotted by many liberals.
At least eight died during demonstrations outside the presidential palace this month.