Egypt's Islamists in slim poll victory
Their slogan throughout the referendum build-up was a call for "stability" so that the economy could be put right.
Those Egyptians, along with others who voted No, may be more receptive to opposition charges that Mr Morsi is mishandling the economy and out of touch with the poor while he pushes through measures seen as favouring the Brotherhood and its allies.
That is likely to be an increasingly fierce battleground as the parliamentary election looms.
"The opposition comes out of this in a stronger position," said Shadi Hamid of the Brookings Doha Center. "Morsi and the Brotherhood were hoping for a decisive victory to claim vindication. But they are not going to be able to do that.
"This is a good result for Egypt's democratic process," he added. "It shows non-Islamists can gain ground against Islamists in democratic elections. They do have an interest in shifting the battle from the street to institutionalised politics."
There are signs of a trend. When a first, temporary, constitutional framework was put to the vote just weeks after Mubarak's downfall - also opposed by liberals and backed by Islamists - it secured more than 75 per cent of the vote.
Islamists then swept up a big majority in voting for the interim parliament, securing about 70 per cent of seats. But Mr Morsi's presidential win in June was less convincing; he took about 52 per cent of votes against a Mubarak-era general.
Yesterday's vote confirms that non-Islamists are starting to form a more credible challenge. Yet more liberal-minded politicians still have their work cut out.
The Brotherhood, founded in the 1920s, has built up an unrivalled social support and charity network across Egypt, expanding even as Mr Mubarak and his predecessors oppressed them.
That has helped them do well in the more localised politics of parliamentary polls, turning out the vote in neighbourhoods.
Liberals have no such history of organisation. Though the Popular Current movement of leftist Hamdeen Sabahy and Mohamed ElBaradei's Constitution Party have broadened their appeal, they boast nothing like the grass-roots presence of the Islamists.
Mr Morsi may also have a chance to weather the economic storm. At least some investors may be happy to see a constitution in place as it resolves one of their worries that the transition to democracy was drifting, even if plenty more concerns remain.
After the unofficial referendum result, Egypt's benchmark stock market index rose 2.7 per cent, though the pound is still bumping along at its weakest against the dollar in eight years.
"Given how severe the downside risks seemed just a week or so ago, a fiercely contested referendum attracting a decent turnout is a positive outcome," said HSBC economist Simon Williams.
"However polarised the debate may have become, if it stays within the institutions of the state, then there is some prospect of the political transition moving forward," he said.
Nevertheless, the result does not mean an end to protests.
A spokeswoman for the Popular Current, Heba Yassin, said Egyptians were still "inflamed and furious" and added that the "final word will come from the Egyptian street".