An October surprise might take place in Iraq that could affect the outcome of the U.S. presidential election. There could even be two October surprises.

But, in this polarized political season, it’s not clear which candidate would be helped or hurt.

Iraqi officials are predicting that insurgents may try to influence the U.S. vote by doing something particularly violent just before Nov. 2. “There could be an October surprise – a big bang in Baghdad,” I was told from Baghdad by Zuhair Humadi, the secretary-general of the Iraqi cabinet.

One possible move by the insurgents could be an effort at deep penetration of the Green Zone, the tightly protected area of Baghdad where the Iraqi government, the U.S. Embassy and military headquarters, along with the United Nations election team, are based. Iraqi and U.S. officials fear there may be an effort to duplicate the 1968 Tet Offensive in Vietnam, in which North Vietnamese forces invaded regional capitals and managed to penetrate the U.S. Embassy in Saigon.

The North Vietnamese were pushed back and took huge casualties. But the fact that enemy forces could reach the U.S. Embassy was a public relations disaster for the presidency of Lyndon B. Johnson.

Despite tight security around the Green Zone, two suicide bombings within the perimeter last week killed 10 people. Many Iraqis live and work inside the zone, and it clearly can be penetrated.

During a trip to Iraq in June, U.S. military guards inside the zone told me that a jeep had been stopped within the perimeter with four men falsely claiming to be Arab journalists. Their hands tested positive for explosives and they were found to have weapons in their Baghdad hotel room. I never verified this story or learned how it ended, but the risk of attack inside the zone is high.

How such an attack would affect the U.S. election is less apparent. It could lead voters to rally ‘round Bush or convince them that a change in Iraq strategy is needed. Or, with voters so sharply divided, it might simply confirm their previous opinions.

The second surprise could occur if the U.S. military and Iraqi leaders make a breakthrough in pacifying the insurgent stronghold of Fallujah.

Prime Minister Ayad Allawi has been negotiating with tribal leaders from Fallujah in hopes of getting them to turn over hard-core insurgents.

“Not so many are willing to be considered in the same breath with (al Qaeda supporter Abu Musab) al-Zarqawi,” I was told by Iraqi Finance Minister Adil Abdel-Mahdi on a recent visit to Washington.

“They are distancing themselves from cutting off heads and this kind of behavior,” he added. “They will have to choose between (entering) politics and violence.”

But the government’s talks with the Fallujah sheikhs have faltered over demands that they turn over Zarqawi. And, even if Zarqawi and his ilk left, it isn’t clear who would then run restive Fallujah. The last time U.S. forces made a deal with a group of Fallujah forces to run their town, the Fallujans joined the insurgents.

Abdel-Mahdi suggested that there might be a military attack on the city if negotiations failed. “Yes, there will be an offensive before the elections,” he said, adding that much of the civilian population was leaving in advance of the fighting. But this would be risky, since no one knows if Iraqi forces will fight inside Fallujah. (Most refused during a U.S. offensive in April.)

Nothing would look worse for the administration than to become embroiled in a messy military offensive right before the elections. A negotiated settlement in Fallujah, on the other hand, might boost Bush’s re-election prospects, even though it could fall apart thereafter.

Meantime, high oil prices have given the Allawi government a small financial cushion to spread around Iraqi trouble spots to try to calm insurgents. Oil money goes primarily to pay the government’s basic expenses and government salaries, since most Iraqis with jobs work for the state. But Iraqi officials tell me the oil windfall is permitting them to spend tens of millions of dollars in Baghdad’s Sadr City, in Najaf, and Samarra, to create jobs and buy off troublemakers.

This jobs program isn’t likely to persuade those insurgents who want to influence U.S. elections. So look for them to make a big bang in October or try to thwart a solution in Fallujah. How either move will affect the U.S. polls is anybody’s guess.