The most important aspect of the battle for Fallujah may be its aftermath.
As the fighting following the fall of Baghdad has turned out to be crucial, so the struggle to spread and consolidate any gains made by the assault on insurgent-riddled Fallujah could be key to Iraq's future, say US officials and military experts outside government.
That's because other Iraqi cities are watching. If US-led forces take Fallujah with relative quickness and efficiency, Samarra, Ramadi, and other restive regions may decide that harboring insurgents isn't worth it. But if the attack stalls, or causes large numbers of civilian casualties, moderate or politically uncommitted Iraqis might decide that the guerrilla fighters could end up winners, after all.
Nineteen months after the ouster of Saddam Hussein, Iraq thus may have reached a tipping point in regard to the attitude of its ordinary civilians.
"This is being done for not only its effect on Fallujah, but for its demonstration effects ... on other places resembling Fallujah," says a retired general and strategist still connected with the Pentagon.
For now the fighting in Fallujah, carried largely by American infantry and marines with support from Iraqi government units, appears to have only increased the political complexity in Iraq.
Pentagon officials have long indicated that they could not allow Fallujah to remain an insurgent stronghold with elections now only months away. Confronting insurgents via direct assault may just cause them to melt away, and Fallujah is far from the only no-go zone for US forces in the country. But US officials argue in essence that they have to start somewhere.
"You cannot have a country that is free and democratic ... if you have safe havens for people who go around chopping people's heads off," said Secretary of Defense Donald Rumsfeld at a Pentagon press conference on Monday.
In April, a US attempt to capture and hold Fallujah was called off, mostly because the Iraqi Governing Council, then in office, objected to it. The current interim Iraqi prime minister, Iyad Allawi, vows that won't happen this time - though the pressure on him is increasing quickly. On Tuesday, a group of Sunni clerics announced they will boycott the upcoming election. The Iraqi Islamic Party, the dominant Sunni group supporting the interim government, now says it is withdrawing its backing due to the assault of Fallujah, in the heart of the Sunni triangle.
Stomping on Fallujah is, in fact, exactly the opposite of what the US should do if it wants to lure Sunnis into the Iraqi political process, argues a former CIA official with 25 years experience in the region.
The way to bring the insurgency to an end, or at least reduce it to a few bitter-enders and foreign fighters, is to convince Sunnis that they have a role to play in the new Iraq, says Whitley Bruner, now director of government relations for Diligence, a security and information company in Washington. Destroying Fallujah in order to save it won't work.
"If you try to beat them into submission, they will continue to fight, and you can't ... stay there forever," says Mr. Bruner.
Furthermore, it's possible that the insurgents will not fight to the last man in Fallujah, but will withdraw and regroup elsewhere, waiting for a time and place to strike again. Samarra has already seen something of this dynamic of retreat and resurgence. Elsewhere, Mosul, Ramadi, and other cities might see an upsurge in violence prior to scheduled elections.
"The insurgents have every incentive not to be destroyed in Fallujah if they can move outside into the rest of Al Anbar province," notes Anthony Cordesman, a military expert at the Center for Strategic and International Studies in Washington, in a written analysis of the current military situation in Iraq.
That said, the US military is gearing up for a series of operations, Pentagon officials hint. Fallujah may not be the last area to face renewed assault. "It's a tough business, and I think it's going to take time," said Secretary Rumsfeld on Monday.
While insurgent units may not stand and fight a pitched military battle, as if they were mechanized infantry confronting US forces in open maneuver warfare, constant harassment and attack might still degrade their abilities over time.
Simply standing by and allowing insurgents to continue with the level of violence they have sustained in recent months is unacceptable, according to US military officers. "We have to get after their leadership, we have to get after their money, we have to get after their operational communications," said Air Force Gen. Richard B. Myers, chairman of the Joint Chiefs, earlier this week.
But it may be the battle after the battle that determines which direction Fallujah and other areas of Iraq not now entirely under government control will slide. And that battle - consisting of the stability and nation-building activities that have proven so difficult to this point - will be increasingly out of US hands. "It will be Iraqi politics, governance, economic and aid activity, and military and security forces that ultimately win or lose," says Mr. Cordesman.