US is keen to show that Iraq's own forces can counter a wave of insurgent attacks.
Continued US and Iraqi government military offensives in Iraq may reflect an overall attempt to restore the notion that time is running out for the Iraqi insurgency.
In recent months a continued surge in suicide bombing and other insurgent-spawned violence has swept away much of the positive feeling and political momentum generated by January's Iraqi election. US commanders have become increasingly reluctant to analyze when, or even if, the insurgents might be finally defeated.
Turning this trend around, and restoring the atmosphere of optimism, may well have become a top priority for both Washington and Iraq's new leaders. US officials in particular are keen to highlight progress in the development of Iraq's military, as the degree to which Iraq is taking part in its own defense appears to be a crucial determinant of American public attitudes towards the war.
"The US public is looking for success, and success to them means cooperating with the Iraqis," says Christopher Gelpi, a Duke University expert on public opinion about Iraq.
On Tuesday President Bush himself insisted that despite mounting casualties and such tragedies as the kidnapping and subsequent death of the Iraqi governor of Anbar province the Iraqi government is "plenty capable" of defeating the insurgents.
The January vote was a hinge of Iraq's history, insisted Mr. Bush. The upsurge in violence which followed it has stemmed from desperation on the part of those who see themselves on the eventual losing side.
"What the insurgents fear is democracy, because democracy is the [opposite] of their vision," said Bush in a Rose Garden appearance.
Outside of Baghdad, US forces continued offensive operations meant to counter Islamist insurgents of Abu Musab al-Zarqawi. Some 125 insurgents have been killed in these actions, according to the US. However, a tape alleged to be the voice of Zarqawi himself said that he was fine despite a "light" wound inflicted by the US.
Meanwhile, in and around Baghdad the Iraqi-led counter-insurgent Operation Lightning entered its third day.
So far, the effect of this offensive has been difficult to interpret. Government officials point to the arrest of hundreds of suspected insurgents in the last two to three days, yet the promised security cordon around the city has thus far failed to materialize.
By Tuesday, larger-than-usual numbers of soldiers and police could be seen along major thoroughfares, but most appeared to be resting in whatever shade they could find, rather than actively monitoring passing cars. Traffic was flowing normally, with no more or less congestion than usual.
Despite the government's promise of 675 fixed checkpoints and additional roving checkpoints, motorists said they were able to drive from one end of the city to another without actually being stopped or searched.
One danger of the new crackdown might be increased sectarian violence. The new Iraqi government is dominated by Shiite Muslims with ties to Iran, and its target is an insurgency that despite the presence of Islamist fighters remains overwhelmingly Sunni Muslim.
The concern here is that even moderate Sunnis might harden their attitude toward the possible participation in government if they perceive that Sunnis are being unfairly singled out. Monday's mistaken arrest by US forces of a prominent Sunni Muslim political leader who has urged compromise, Mohsen Abdel Hamid, unfortunately aggravated Iraq's sectarian tensions.
Furthermore, Zarqawi and his foreign Islamist fighters would undoubtedly be only too happy to see these tensions increase.
"The insurgency already has long been a low-level civil war, and is being driven towards a broader Sunni vs. Shiite conflict by Islamist extremists," writes Center for Strategic and International Studies expert Anthony Cordesman in a draft of a new book on the evolving insurgency.
According to Cordesman, the main body of Iraq insurgents has learned to create a continued level of violence as a means to try and destabilize the Iraqi situation. They have improved methods of attack through such means as digging holes in roads, inserting bombs, and then paving them over so as to make them undetectable by the eyes of US troops on patrol.
Senior US officers have become far more circumspect in their predictions since the heady days following the January vote. They now talk about "years" of combat, Cordesman notes.
"It is still far from clear whether the US and Iraqi government will be able to decisively defeat the various insurgent groups," writes Cordesman.
Vice President Dick Cheney, for his part, insisted in a broadcast interview that the insurgents would be defeated by the end of President Bush's second term.
"I think they're in the last throes, if you will," Mr. Cheney told CNN.
For US military forces, the most important lesson of recent experience may be the need to work closely with the Iraqis.
This really seems to have been learned within the past year, since the uprising in Fallujah, the brief Shia insurgency in Sadr City and Najab, and the handover to a sovereign Iraqi government. Since then, far more US money and energy has been dedicated to upgrading the Iraqi security forces. Perhaps the outcome will be seen in Operation Lightning, where around 10,000 US troops are said to be available to support the claimed 40,000 Iraqis taking part.