That would make the 275-seat assembly's first order of business an easy one -- ratifying a set of prearranged nominations rather than getting bogged down in acrimonious political fighting.
But after some early momentum, the parties appear to still be far from reaching their goal.
The lead player in the negotiations is the United Iraqi Alliance, endorsed by preeminent Shi'ite Grand Ayatollah Ali al-Sistani. The alliance won the most seats in the National Assembly but fell short of the two-thirds majority needed to make sure its candidate, Ibrahim al-Ja'fari, becomes prime minister. So it has sought to secure the support of the next biggest bloc, the Kurdish coalition.
But the deal-making process between the two sides is reported to have only grown more difficult with time. One of the thorniest issues is Kurdish demands to clarify the future status of the ethnically mixed northern city of Kirkuk.
Jalal Talabani, the Kurds' candidate for Iraq's next president, put his feelings about Kirkuk this way last month: "We believe that Kirkuk [city], in terms of geography, is situated in the Kurdistan region. That means that we must respect the rights of all so that the coexistence in Kirkuk is a brotherly one, based also on the principle of consensus between [various] communities of the society in Kirkuk."
The Kurds regard Kirkuk as their natural capital and many would like to ultimately expand the Kurdish-administered area of northern Iraq to include it.
But there are other problems, too. The secular Kurdish coalition has said it cannot back the United Iraqi Alliance -- which includes powerful Shi'ite religious parties -- unless it is assured the alliance will not try to impose Islamic principles on Iraqi public life.
The other main player in the political jockeying is current interim Prime Minister Iyad Allawi, who wants to head the next government, too. His party came in third in the national elections and also is negotiating with the Kurds for support. But so far there are no reports of a deal.
Allawi vowed last week to remain in the fray despite calls from some opponents to simplify matters by withdrawing his candidacy. "First of all, I will not withdraw [my nomination as prime minister in the next government] because, as you know, we fought against Saddam's regime and now we have another important assignment, which is the building of Iraq," Allawi said.
Now, with the parties unable to agree on a new order, prospects are rising that the deadlock might continue into the National Assembly itself. If so, the stalemate could see Allawi running the country in a caretaker role until a compromise is found.
Meanwhile, Iraq's election winners have yet to announce publicly any measures to increase Sunni representation in their ranks or in the National Assembly.
Top Iraqi political figures have said they will reach out to the Sunni community in the wake of the 30 January elections. The elections saw Sunni voters largely stay away from the polls.
For news, background, and analysis on Iraq's historic 30 January elections, see RFE/RL's webpage "Iraq Votes 2005".