If parliament fails to propose a candidate from inter-party negotiations to replace outgoing Adel Abdel Mahdi, then President Barham Saleh has the right to appoint a premier himself.
But if lawmakers do not approve his choice and the post remains vacant at midnight, then the constitution will place Saleh himself in the role, though for just 15 days.
The current parliament is the most divided in Iraq's recent history. On Wednesday, deputies failed to agree on amending the electoral law - the only significant reform proposed by authorities to appease protester demands - rescheduling it to its next meeting on Monday.
Following elections last year, no bloc was able to establish the majority necessary to put its nomination for premier to a vote.
Instead, the parties agreed on an independent candidate with no base of his own - Abdel Mahdi.
A consensus choice, Abdel Mahdi lasted a year in the role before resigning in November after two months of unprecedented anti-government protests in the capital Baghdad and Shia-majority south, marked by 460 killed and 25,000 injured.
Despite his resignation, protests have continued in the face of brutal repression, killings and abductions, and a chilly winter.
Unyielding protesters
Several names for the premiership are still circulating hours before the expiration of the constitutional deadline.
But all are insiders in a political system rejected in its entirety by protesters, who also oppose the growing influence of Iran, a powerbroker in Iraqi politics.
Outgoing Higher Education Minister Qusay Al-Suhail has for several weeks been presented by officials as the candidate of Iran.
A former key member of Shia cleric Muqtada Sadr's movement, Suhail rejoined the State of Law Alliance of former prime minister Nouri al-Maliki - close to Iran and enemy of Sadr - and seems to become the favourite for the premiership.
But nothing is sure after weeks where each day a leading candidate ends up being dismissed. In Baghdad's Tahrir Square, posters display the rejected candidates with their faces crossed out in red.
On Wednesday, Mohammed al-Soudani, a former minister and ex-governor, presented himself in Najaf to be endorsed by Grand Ayatollah Ali Sistani - longtime kingmaker in Iraqi politics. But he was rejected, according to sources in the Shiite shrine city.
Wary of the anger on the street, the 89-year-old cleric, the highest religious authority for the majority of Iraqi Shia, had already said he did not want to be involved in the formation of the new government.
11th hour asset
Several politicians told AFP that Saleh held a card for the 11th hour: intelligence chief Moustafa al-Kazemi, a shadowy figure seen as backed by the United States.
On Wednesday, Fayeq Al-Sheikh Ali - an outspoken liberal lawmaker who defends the right to drink alcohol and is critical of Iraq's endemic corruption - presented his own nomination to the president.
Far from the party summits, the day before he had asked in a Twitter survey, "Should I submit my own candidacy?" to which 73 percent of nearly 100,000 voters replied, "yes".
The security situation meanwhile has worsened, with recent rocket attacks on American bases.
Ten security incidents in under two months have prompted the US to send military reinforcements to the heavily-fortified Green Zone in Baghdad, home to its embassy.
US diplomatic staff have been reduced, with the consulate in Basra closed.
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