BAGHDAD - The Iraqi parliament on Sunday failed to resolve an impasse threatening to delay the country's election in January, which could affect the U.S. military's plans for a partial pullout next year.

There are only a couple of days left for parliament to address Vice-President Tareq al-Hashemi's veto of an election law, as the law must be passed 60 days before a vote and January 23 is viewed by Iraq's majority Shi'ite Muslims as the last possible date in January for the ballot to take place.

If no resolution is found, Iraq may have to delay the election for a month until after the Shi'ite religious festival of Arbain, a move that western diplomats and U.N. officials have warned would be unconstitutional.

I think tomorrow will be crucial and the issue will be resolved, said Khalid al-Attiya, deputy speaker of parliament. There are no agreements but there are ideas and I hope we will agree on a specific project tomorrow.

The election is viewed as a milestone for Iraq as it emerges from years of sectarian bloodshed since the U.S. invasion in 2003 and starts to stand on its own feet ahead of a full U.S. withdrawal by December 31, 2011.

Privately, Western and Iraqi officials say a short delay in holding the ballot might not be a bad thing as it would give the electoral authorities more time to prepare.

But the constitution stipulates that the next election should be held by January 31, and breaching that barrier could set a dangerous precedent that might be exploited in the future by a would-be strongman, disinclined to hold a scheduled election.

A major delay might also affect U.S. plans to end combat operations by August 31 next year, as U.S. military commanders want to retain a sizeable force in Iraq until the next government is in place and the security situation is clear.

VOTES ABROAD

Hashemi, a Sunni Arab who is one of three members of a presidential council with veto rights, rejected the election law because he said it did not give enough representation to Iraqis who fled abroad when the U.S. invasion triggered sectarian bloodshed. Many of the exiles are Sunnis.

Parliament is discussing whether it can reject Hashemi's veto and send the law back to the presidential council or whether it has to amend the law first.

If it decides to amend the law, there is a risk that other parties will seek additional changes.

Iraq's minority Kurds have said they might boycott the election unless their three semi-autonomous provinces in northern Iraq are given more seats.

The election law was approved on November 8 after weeks of wrangling between Kurds, Arabs and Turkmen over how to hold the vote in the city of Kirkuk, which they dispute. U.S. diplomats and U.N. officials lobbied energetically for passage of the law.

We only have 48 hours to end this impasse, otherwise an election by the end of January will be impossible, said Abbas al-Bayati, a lawmaker of Prime Minister Nuri al-Maliki's ruling Shi'ite alliance.

(Writing by Michael Christie; Editing by Janet Lawrence)