Parliament broke for its summer recess on Wednesday without passing the contentious bill, which has been stalled over differences on how the northern province of Kirkuk should be governed.
The UN had proposed that the polls in Kirkuk be postponed until December 2009 but that polls in Iraq's 17 other provinces go ahead as scheduled.
However the deal failed to win approval from various Arab and Turkmen factions.
Mahmud al-Mashhadani, parliament's speaker, has ordered a committee of politicians to continue working on the draft law until the body reconvenes on September 9, but infighting has cast doubt on whether a deal can be reached.
Said Arikat, spokesman for the UN Assistance Mission for Iraq, said that holding the election on time would now be "impossible" and that the outlook for an election at all this year was at best uncertain.
"If the law is not passed in the next few days, it will be very, very difficult to hold the election before the end of the year," he said, adding that the UN would work to bring about an agreement.
"It was clear since July that it would be impossible to hold the election in October," Arikat said.
The disagreement centres on an article of the original draft that would have divided power equally amongst the province's Arab, Kurd and Turkmen communities. It has been opposed by the Kurds on the basis of their superior numbers and historical claims to the city.
Parliament approved that draft last month after Kurdish politicians and some Shia ministers walked out, but the presidential council, led by Jalal Talabani, the president and an ethnic Kurd, vetoed the bill.
On Thursday, several hundred Turkmen took to the streets waving Iraqi flags and calling for the removal of Staffan de Mistura, the UN envoy for Iraq, accusing him of favouring the Kurds.
"We ask the UN to investigate Kirkuk events, and to change its 'Kurdish representative' Staffan de Mistura in Iraq," one banner read.
The protest was the latest in a series of political rallies in Kirkuk.