The officers - combat veterans who are experts in counter-insurgency - are charged with implementing the "new way forward" strategy announced by George Bush on January 10. The plan includes a controversial "surge" of 21,500 additional American troops to establish security in the Iraqi capital and Anbar province.

But the team, known as the "Baghdad brains trust" and ensconced in the heavily fortified Green Zone, is struggling to overcome a range of entrenched problems in what has become a race against time, according to a former senior administration official familiar with their deliberations.

"They know they are operating under a clock. They know they are going to hear a lot more talk in Washington about 'Plan B' by the autumn - meaning withdrawal. They know the next six-month period is their opportunity. And they say it's getting harder every day," he said.

By improving security, the plan's short-term aim is to create time and space for the Iraqi government to bring rival Shia, Sunni and Kurd factions together in a process of national reconciliation, American officials say. If that works within the stipulated timeframe, longer term schemes for rebuilding Iraq under the so-called "go long" strategy will be set in motion.

But the next six months are make-or-break for the US military and the Iraqi government. The main obstacles confronting Gen Petraeus's team are:

· Insufficient troops on the ground

· A "disintegrating" international coalition

· An anticipated increase in violence in the south as the British leave

· Morale problems as casualties rise

· A failure of political will in Washington and/or Baghdad.

"The scene is very tense," the former official said. "They are working round the clock. Endless cups of tea with the Iraqis. But they're still trying to figure out what's the plan. The president is expecting progress. But they're thinking, what does he mean? The plan is changing every minute, as all plans do."

The team is an unusual mix of combat experience and academic achievement. It includes Colonel Peter Mansoor, a former armoured division commander with a PhD in the history of infantry; Colonel HR McMaster, author of a well-known critique of Vietnam and a seasoned counter-insurgency operations chief; Lt-Col David Kilcullen, a seconded Australian officer and expert on Islamism; and Colonel Michael Meese, son of the former US attorney-general Edwin Meese, who was a member of the ill-fated Iraq Study Group.

Their biggest headache was insufficient troops on the ground despite the increase ordered by President Bush, the former official said. "We don't have the numbers for the counter-insurgency job even with the surge. The word 'surge' is a misnomer. Strategically, tactically, it's not a surge," an American officer said.

According to the US military's revised counter-insurgency field manual, FM 3-24, written by Gen Petraeus, the optimum "troop-to-task" ratio for Baghdad requires 120,000 US and allied troops in the city alone. Current totals, even including often unreliable Iraqi units, fall short and the deficit is even greater in conflict areas outside Baghdad.

"Additional troops are essential if we are to win," said Lt-Col John Nagel, co-author of the manual, in an address at the US Naval Institute in San Diego last month. One soldier for every 50 civilians in the most intense conflict areas was key to successful counter-insurgency work.Compounding the manpower problems is an apparently insurmountable shortage of civilian volunteers from the Pentagon, state department and treasury. They are needed to staff the additional provincial reconstruction teams and other aid projects promised by Mr Bush.

The cut in British troops in southern Iraq, coupled with the actual or anticipated departure of other allies, has heightened the Petraeus team's worries that the international coalition is "disintegrating" even as the US strives to regain the initiative in Iraq, the former official said.

Increased violence in the south is expected, caused in part by the "displacement" of Shia militias forced out of Baghdad by the US crackdown. American and Iraq forces entered the militant Shia stronghold of Sadr City on Tuesday for the first time since the surge began. No other major operation has yet been attempted there but "we or the Iraqis are going to have to fight them", one US officer said.

According to a British source, plans are in hand for the possible southwards deployment of 6,000 US troops to compensate for Britain's phased withdrawal and any upsurge in unrest.

Morale is another concern in the Green Zone headquarters: American forces are preparing for a rise in casualties as the crackdown gathers pace. In a message to the troops after he assumed overall command last month, Gen Petraeus praised their sacrifices while warning of more "difficult times" to come.

"We serve in Iraq at a critical time ... A decisive moment approaches. Shoulder to shoulder with our Iraqi comrades we will conduct a pivotal campaign to improve security for the Iraqi people. The stakes could not be higher," Gen Petraeus said.

"It's amazing how well morale has held up so far," the former official said. "But the guys know what's being said back home. There is no question morale is gradually being sapped by political debates."

The advisers are also said to be struggling to prevent the "politicisation" of the surge by the Shia-dominated government. The fear is that any security advances may be exploited to further weaken the position of Baghdad's Sunni minority.

Despite progress this week on a new law sharing Iraq's oil wealth, the Petraeus team believes the government is failing to work hard enough to meet other national reconciliation "benchmarks" set by Mr Bush.Yet it is accepted that the US is asking the prime minister, Nouri al-Maliki, to do what most politicians in normal circumstances would refuse to contemplate. "What we're doing is asking Maliki to confront his own powerbase," one officer said.

Possibly the biggest longer term concern of Gen Petraeus's team is that political will in Washington may collapse just as the military is on the point of making a counter-insurgency breakthrough. According to a senior administration official, speaking this week, this is precisely what happened in the final year of the Vietnam war. Steven Simon, the national security council's senior director for transnational threats during the Clinton administration, said a final meltdown in political and public backing was likely if the new strategy was not seen to be working quickly.

"The implosion of domestic support for the war will compel the disengagement of US forces. It is now just a matter of time," Mr Simon said in a paper written for the Council on Foreign Relations. "Better to withdraw as a coherent and at least somewhat volitional act than withdraw later in hectic response to public opposition... or to a series of unexpectedly sharp reverses on the ground," he said.

"If it gets really tough in the next few months, it will throw fuel on the fire in Washington," the former official said. "Congress will be emboldened in direct proportion to the trouble in Iraq." If the policy was not judged to be working by Labor Day (the first Monday in September which marks the start of the new political year), Mr Bush could lose control of the policy to Congress and be forced to begin a phased pull-out, he suggested.

A senior Pentagon official said this week that it was too early to gauge the strategy's chances of success - but preliminary reports were encouraging. "There are some promising signs. There is a new overall Iraqi commander in Baghdad. A number of joint operations have just begun. The number of political murders has fallen. Iraqi forces are showing up as promised, admittedly a little bit under strength, and are taking up some of the responsibilities that Maliki said he would,"he said. "We have to be realistic. We're not going to stop the suicide bombers and the roadside explosive devices for some time. And the military alone are certainly not going to solve the problem. Maliki has to meet the benchmarks. A civilian surge is needed, too. The Iraqis have to do it themselves."

US officials say they also have rising hopes of a breakthrough in Sunni-dominated Anbar province where tribal chiefs are increasingly hostile to al-Qaida and foreign fighters - and are looking to build bridges with moderate Shias.

But this week's US decision to join talks on Iraq with Iran and Syria, after previously refusing to do so, is nevertheless seen as an indication of the administration's growing alarm at the possibility of a historic strategic failure.