The assembly began going through the charter yesterday in a process expected to end on January 14, the third anniversary of the ouster of Zine El Abidine Ben Ali in the revolution that sparked the Arab Spring.
Leading Francophone daily La Presse said disputes among MPs, interruptions and procedural problems made for "distressing scenes," suggesting the deadline may not be met.
"Tunisians who expected to see scenes of solemnity as the constitution was being discussed" were disappointed, it said, comparing scenes in the assembly to "a wild arena in which every cheap shot is permitted."
The tight deadline set for its adoption could end months of political crisis and further distance Tunisia from the chronic instability plaguing other countries in the region rocked by regime change.
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"Other obstacles will certainly appear, making the birth of the new constitution painful," it predicted.
The Maghreb daily retained some optimism, but noted that the January 14 deadline would probably not be met.
Yesterday's first session resulted in lawmakers approving the title of the charter, by 175 votes out of the 184 MPs present, and the first three paragraphs of the preamble only.
They are also due to scrutinise the 146 articles finalised in June and some 30 key amendments drafted during the recent negotiations.
Another 200 amendments have also been proposed, including an attempt to make Islamic sharia law a main source of legislation, but these are thought to have little chance of passing.