George W. Bush's political future - and his role in history books - may depend on whether a change of flags changes what Americans believe about the meaning of the US involvement in Iraq.
The administration hopes that as the former US occupation authority begins to fade into the background, and US troops pull back into more static defense, US voters will see a mission as at least partly accomplished. This best-case scenario will be much more likely if the new Iraqi government gains some legitimacy and control over insurgents, of course.
In the short run, there could be at least a psychological easing of burdens on the domestic front, as Americans feel some pullback from the full weight of responsibility for Iraq's future. US troops will certainly still be at risk, but the hope will be that an Iraqi government and Iraqi security forces will take on the brunt of the challenges.
The danger is that as US power begins to recede, the resultant vacuum will be filled not by new local authorities, but by chaos. Then a US public that already disapproves of policy in Iraq might sour further on the whole adventure, whether US military casualties decline or not.
"We're going to continue to get some very serious events that are going to affect America and some people are going to say, 'Hey, I thought this was over,' " says Gordon Newby, a professor of Middle Eastern studies at Emory University in Atlanta.
Some 15 months after he first ordered the invasion of Iraq, President Bush on Monday praised the handover of power as an important event that signaled the beginning of the end of the US presence.
The US had kept its word to deliver freedom and a new government to the country, said Mr. Bush.
"The Iraqi people have their country back," he said from Istanbul, Turkey, where he is attending a NATO summit.
Meanwhile, military officials in Washington were indicating that the change in flags would also mark a change in tactics by US troops on the ground.
The Iraqis themselves will now pick up more and more street patrol security duties, they insisted. US forces will focus more on the protection of oil pipelines, the electrical grid, and other key infrastructure components. They will continue to provide security for Iraq's newly appointed leaders.
As for the policies those leaders will implement, that's something for the Iraqis themselves to mull over, suggest US officials. Important items such as the degree of autonomy granted Kurds won't be dictated from Washington, according to Bush administration officials.
The US will step back "and let the Iraqis figure out a lot of these issues for themselves," said National Security Adviser Condoleezza Rice over the weekend.
But the reality is that the US will remain a major force in Baghdad, if not technically an occupying power. The tens of thousands of US troops remaining in the country are perhaps a better indicator of the balance of things than is the departure of former administrator L. Paul Bremmer.
The fate of these troops may now become a crucial indicator of the direction of US public opinion, say some experts. The biggest marker for many voters as to the success or failure of Iraq may be whether the sad funerals for service personnel continue in the Midwestern and Southern towns and regions that contribute disproportionately to armed service strength.
"The threshold for Americans is simply Americans dying over there," says Carole O'Leary, a Middle East expert at the American University in Washington.
After all, in recent months the steady toll has taken a corresponding toll in approval ratings for the war.
Most recent national polls have found that a majority of respondents disapprove of the way Mr. Bush is handling Iraq. Last week a CNN/USA Today Gallup poll found that 54 percent of those asked thought it a mistake to send troops to Iraq in the first place.
Those are dangerous numbers for an incumbent this close to an election. Furthermore, that rating could decline even more if the new interim government in Iraq is ineffective, or if the country's very existence within current borders is thrown into question.
Thus the period between now and implementation of a formal constitution and elections is a crucial one. The US has begun the process of pulling out of Iraq while some of the most difficult questions of governance of the country remain unresolved - particularly the degree of autonomy Kurdish areas will retain in the new Iraq.
The US doesn't really have any idea what form of government that Iraq's potentially largest voting bloc, Shiite Muslims, wants, points out Jean-Robert Leguey-Feilleux, a professor of political science at St. Louis University in Missouri.
How will Kurds fare in a possible Shiite-dominated political system? How would Sunni Muslims, the former power center of the country, feel about it? Will the Baath party make a comeback?
"In other words, the future is very uncertain," says Professor Leguey-Feilleux.
Thus the irony for the Bush administration: It has partly handed its future into the hands of groups and factions over which it will have declining influence. In some ways, the White House's most uncertain period of its whole Iraq involvement may have just begun.