However the streets of Tunisian cities appeared calm on Thursday after major parties decided earlier in the week to avoid any major protests or confrontations for now, and after Saied imposed stricter COVID-19 measures.
Though the biggest parties in parliament, including the moderate Islamist Ennahda, have accused Saied of a coup, the UGTT labour union has so far avoided direct criticism of his actions but has urged him to stick to the constitution.
Saied has rejected charges of a coup, saying his actions were justified by an emergency provision in the constitution and that parliament will be frozen only for a 30-day period.
The UGTT has tapped economic, political and constitutional law experts to find a way through the crisis that they can present to the president, union officials said. Saied held talks with the union on Tuesday in one of his first major meetings.
The UGTT won a Nobel Peace Prize in 2013 for its work as part of a civil society "quartet" that helped negotiate an end to an earlier democratic crisis.
Saeid's actions generated an immediate outpouring of support late on Sunday in major cities, where people had grown increasingly angry at the government's perceived inept handling of the economy and COVID-19 crisis.
An opinion poll published in Tunisian media on Wednesday by Emhrod, a company whose surveys before the 2019 election were close to the eventual results, said nearly nine in 10 Tunisians backed his actions.
Years of failure by the political elite to meaningfully address the country's many problems, aggravated by the pandemic, have infuriated ordinary Tunisians and helped spur backing for Saied on Sunday.
But people do want to see results.
"There is no blank cheque. It's true that we have faith in him and we believe in his good intentions, but the implementation remains an obstacle. He must come out every day to tell us what he will do," said Hatem Belkadhi, a man speaking on a central Tunis street.
There is no indication that Saied will find it any easier to handle the country's economic problems than successive past governments.
While foreign lenders demand clear economic reforms to put Tunisia's fiscal position into better order, the UGTT is ready to mobilise against moves that rebound on poorer people - including subsidy cuts or reductions to the public wage bill.
Saied's advisers lack experience in direct governance, while the difficult decisions that will be needed to manage the situation may undermine his support said Tarek Megerisi of the European Council on Foreign Relations.
"His popularity now is a law of diminishing returns. Everything he does is going to lose him some supporters," he said.
Meanwhile Attayar, a mid-sized political party in parliament, switched on Thursday to voice support for Saied's position having earlier accused him of a coup. It said it understood the exceptional measures and their motives.
(Reporting by Tarek Amara Writing by Angus McDowall Editing by Frances Kerry) ((firstname.lastname@example.org; Reuters Messaging: email@example.com))