Other players are simply fighting to avoid complete political marginalisation or refusing to participate in any arrangement that does not foresee a complete end to the US occupation.
It is painfully clear that legitimising a post-war authority in occupied Iraq will be marred by difficulties, since the country's key players subscribe to their own understanding of the legal framework, according to which they believe Iraq should be governed.
For the US, freedom and democracy in Iraq were and remain important pretences used whenever the role of the US government is questioned.
Sidelining the UN
On 16 October 2003, the US exhibited willingness to concede on the issue of power-sharing in Iraq. On that day, the UN Security Council unanimously adopted US-sponsored resolution 1511, which resolved that the United Nations should assume a "vital role" in post-war Iraq.
However, nearly a month later, Washington seemed to have shelved the spirit of the resolution by forging a side agreement with the Iraqi Governing Council (IGC) that did not include the UN, which once again was rendered irrelevant.
According to the 15 November agreement, regional caucuses would select an Iraqi national assembly by the end of May 2004, which would in turn select a transitional government by 30 June.
Washington's plan to hand over power to a handpicked group of Iraqis was strongly challenged by Iraq's Shia community, who advocates direct elections, through which they hope to emerge on top.
Shia spiritual leader Grand Ayat Allah Ali al-Sistani, a powerful figure who seems to unify many Shia behind his word, rejected the US scheme and reiterated the demand for elections.
He asserted that a handpicked government is destined to remain in Washington's pocket.
"If elections are held under occupation, they will not be fair"
Shaikh Ahmad Abd al-Ghafur
The US is equally alarmed by the prospect of a decisive Shia victory in any future elections.
Although al-Sistani's call for holding elections appears unbending, he showed some flexibility when he agreed to a UN role in examining the feasibility of elections by the proposed 30 June deadline.
However, other Shia leaders, such as Muqtada Sadr, are not as accommodating.
Sadr took on the UN, accusing it of being "dishonest" and of serving only a US agenda.
"I refuse the participation of the United Nations in supervising elections because it is not honest and it follows America," he said.
End occupation first
But the elections debate sparked another set of worries. Many Sunni Muslims, increasingly marginalised by the US occupation authority, fear being victimised by political favouritism played out in Iraq.
Additionally, influential Sunni groups made it clear that their participation in Iraq's political future is intrinsically linked to the withdrawal of US and foreign troops from their country.
Dr Harith al-Dhari, secretary general of the Association of Muslim Scholars (AMS) and Iraq's leading Arab Sunni scholar, has insisted that: "Elections and the transition of power are worthless as long as Iraq is under occupation."
Al-Dhari, whose association was formed after the fall of Saddam's government to represent the interests of the Sunni community, demands "liberation before elections".
Another prominent Sunni figure implied the US was favouring one group and discounting others. Shaikh Ahmad Abd al-Ghafur told worshippers at Baghdad’s Umm al-Qura mosque on 13 February 2004 that the US is favouring one group over others, in a reference to the Shia.
"The Iraqis want elections. That's important. But what's more important is to think about ending the occupation (first) because if elections are held under occupation, they will not be fair," he said.
In an interview with Aljazeera, AMS spokesman Dr Muhammad Ayash al-Kubaisi said sectarianism could be sensed in some statements released by Shia leaders.
Ahmad Chalabi is one of nine
rotating presidents of the IGC
Al-Kubaisi said: "A representative of al-Sistani said it was enough to hold elections in stable Iraqi territories. We can sense sectarianism in such statements.
"It is as if Shia are telling the Americans, 'if we keep our areas calm, we want something in return.'
"We do not want elections to be part of a deal," he insisted.
Even the US-appointed IGC members are not seeing eye-to-eye on the elections quandary.
Ahmad Chalabi, a Shia and a leading pro-US member of the IGC, has called for direct elections before the proposed July handover of power. Another member, Abd al-Aziz al-Hakim, underlined al-Sistani's call for Iraqis to have their political say.
However, Kurdish representatives in the council oppose early elections and wish to safeguard Kurdish political gains through self-rule.
Adding to the tensions, particularity in northern Iraq, Arabs and Turkmen strongly reject the Kurds' intent to maintain a considerable autonomy in northern areas where Kurds are the majority.
The approval of the interim constitution, which granted the Kurds a greater political stake in Iraq, has deepened these worries.
Sami Muhammad Donmez, deputy leader of the Iraqi Turkmen Front coalition of parties, was anything but vague regarding this thorny subject. "We will defend the unity of Iraq until the last moment and the last drop of our blood," he said.
As if occupation and sectarianism are not enough, UN Secretary General Kofi Annan's announcement on 23 February in Japan contributed to an already electrifying situation. Annan said that the UN cannot send its staff back to Iraq until the security situation there has improved. The prospect of that happening anytime soon is slim.
Despite the fact that the UN rejected the Washington-devised caucus model as "not viable", it stopped short of spelling out a mechanism to create a caretaker government.
Annan, who said there should be no ballot in Iraq before the handover of sovereignty to Iraqis by 30 June, did not specify the deadline for holding such elections.
He simply said they would be held "sometime later in the future".
Some say, without a significant and independent UN role, Iraq is likely to remain hostage to conflicting political agendas, quests for power and fears of marginalisation.
On the top, of course, the US and its Coalition Provisional Authority (CPA) are still the ones calling the shots, but they no longer hold all the cards.
Iraq's political players are changing, but who is to say what the end result will be?