It is crunch time in Washington and Baghdad. On Monday General David Petraeus and Ryan Crocker will begin two days of testimony on Capitol Hill about the progress made by President Bush’s “surge” strategy in Iraq. Their report – and how it is received by a Democratic Congress – will not only determine whether Mr Bush can salvage his remaining months in the Oval Office but could also decide the outcome of this war.

What is ‘the surge’?

At the start of the year Mr Bush spurned the advice of the Iraq Study Group, which wanted him to start removing US troops from combat roles, and announced a new strategy. Instead of fewer troops, he would send in more, establishing outposts in the country’s troublespots and suppressing the violence while the Iraqi Shia-led Government promoted reconciliation with the Sunnis. By June, 30,000 more troops had arrived, making a total of 160,000.

Is it working?

General Petraeus: The Times interview

'What sustains you is the Iraqis who are incurring enormous risk to try to achieve the vision of a new nation in an ancient land'

Background

• Comment: General Petraeus polarises Washington

• Q&A: General Petraeus and the surge

• Petraeus dresses right for critical moment

• America can’t just walk away, US general insists

• New US general will copy British 'softly-softly' style

Up to a point. The extra soldiers have contained the sectarian violence in parts of Baghdad and elsewhere. Their presence on the streets has also encouraged Sunnis in Anbar province and other parts of central Iraq to drive out al-Qaeda extremists. The US military has forged an alliance with Anbar’s tribal leaders that has largely pacified one of the most dangerous provinces in Iraq. But violence elsewhere has increased, sectarian hatreds remain high and there is growing conflict between rival Shia militias in the south, where British forces have withdrawn to a final stronghold around Basra airport.

What do the figures show?

It depends on the figures. The US military says that last week there were the lowest number of bombs, killings, improvised explosive devices and other “incidents” in 15 months. Fifty-six US soldiers were killed in August, down from a peak of 120 in May, but nonetheless a high level compared with previous Augusts, when the 43C (110F) heat keeps even insurgents off the streets. The US Government Accountability Office (GAO) says that daily attacks against civilians have remained “about the same” since the surge began in February. The Associated Press counted 1,809 civilian deaths in August, the highest monthly total of 2007. Iraqi government figures suggest that the number of deaths across the country rose by about 20 per cent in August, but dropped sharply in Baghdad, where the “surge” has been focused. A key test will be Ramadan, beginning about September 12, when violence traditionally soars.

The intelligence community has also disputed the way that military chiefs cherry-pick. For instance, if a corpse is found to have been shot in the back of the head it is deemed a “sectarian” murder, but if the bullet went through the front of the head, it is listed as a “criminal” murder.

Has Iraq’s Shia-led Government done its bit?

No. The GAO says that it has met only three of 18 political and security “benchmarks” set by Congress. This score is disputed by the White House. But Mr Crocker has expressed extreme disappointment with Nouri al-Maliki’s “national unity” Government because it is neither national nor united, nor even at times a government.

Sunni ministers have walked out in protest at its failure to promote reconciliation. However, it has belatedly been making an effort, sending Parliament legislation permitting ex-Baathists from Saddam Hussein’s regime to take senior jobs and sharing oil revenues more fairly with Sunni provinces.

Who is General Petraeus?

The top US general in Iraq, brought in to implement the surge. Creative, intelligent and fiercely competitive, he wrote the US military’s new counter-insurgency manual. The 55-year-old believes in winning hearts and minds – not busting down doors – and getting troops out of their bases and into communities. “You can’t secure a population by commuting to the fight,” he says.

And Ryan Crocker?

US Ambassador to Baghdad, a 58-year-old wiry marathon runner who speaks fluent Arabic and has spent much of his distinguished career in the Middle East (he was in the US Embassy in Beirut destroyed by a suicide car bomb in 1983). In 2002 he co-authored a State Department report called The Perfect Storm, which said that invading Iraq would cause bloodshed between Sunnis and Shias.

Have they given any hints about what they will say next week?

They will claim that the glass is half full. For instance, Mr Crocker said this week: “There has been progress in security achieved by the Iraqi and coalition forces, and now there is a need for similar progress on the political front to achieve reconciliation. The US policy in Iraq is stable, and I don’t believe that any quick or major changes will be introduced . . . Iraq and its friends need to be patient.” General Petraeus has told visiting members of Congress that America would be in Iraq in some way “for nine to ten years”. But last week he signalled that some troops could soon be “redeployed, without replacement”.

So, how many US troops are coming home – and when?

Informed speculation is that General Petraeus will recommend withdrawing just one brigade of around 4,000, possibly in January but more likely in March or April. More could follow later, depending on conditions, bringing the total down to 130,000 by the end of 2007.

But wasn’t that going to happen anyway?

Yes, the US military is overstretched and unless tours of duty in Iraq are extended beyond 15 months, a withdrawal has to begin next spring. As General Petraeus said this week: “The surge will run its course – there are limits to what our military can provide.”

How will Congress react?

The Democrats have already been dismissing General Petraeus as a mouthpiece of the White House, saying that next week’s testimony will be the “Bush report”. They are under pressure from activists who do not understand why their mid-term election victory last November failed to end the war. But the Democrats still do not have the 60 votes in the Senate needed to impose a binding withdrawal timetable on Mr Bush.

On the Republican side there are sceptics of the surge and others anxiously eyeing next year’s congressional elections. But most of them are – as yet – unwilling to concede defeat in the war and, after well-marshalled congressional tours of Iraq this summer, support for Mr Bush may be hardening.

An early test will come this autumn when Mr Bush goes back to Capitol Hill asking for another $50 billion (£24.7 billion) in war funding. The Democrats, sensing a loss of momentum, are now discussing a compromise measure sponsored by the moderate Republican Senator John Warner that would set a date for beginning withdrawal without imposing a deadline for completing the job. This would dovetail neatly with the Pentagon’s own scheduled withdrawal plans, but allow the Democrats to save face by telling voters they have helped to (start to) bring (some) troops home (soon).

What does Bush want?

Time. He has given up on achieving much domestically in his final year and knows his legacy will be defined by this war. If he can secure a degree of consensus of keeping troops in Iraq up to, and beyond, the 2008 presidential elections then there is a chance it might just turn around. In contrast to his predecessors over the past 40 years, who were desperate to avoid “another Vietnam”, Mr Bush actively seeks comparisons with Vietnam, saying that America left too early, with devastating consequences for the region.

A controversial take on history maybe, but there is some evidence that he is making headway: behind the “end this war” rhetoric of Democratic presidential candidates such as Hillary Clinton and Barack Obama, the small print of their policies accepts that America will need to keep a substantial residual force in Iraq for many years to come.

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