The new Democratic leadership of Congress has for the first time given explicit warning that it might deny funding for up to 20,000 additional troops in Iraq, which President Bush is expected to order this week.

Nancy Pelosi, Speaker of the US House of Representatives, said that the Democrats would refuse to give him “a blank cheque with no oversight, no standards, no conditions. If the President chooses to escalate the war . . . in his budget request, he is going to have to justify it and this is new for him.”

Her comments threw a cloud over the hopes of securing a bipartisan, cross-party approach to the war that had been raised briefly by publication of the independent Iraq Study Group report last month. This proposed gradual troop reduction and a diplomatic offensive with neighbouring countries in the Middle East. The Bush Administration has since made clear that it remains reluctant to engage in direct talks with states such as Iran and Syria, while also signalling that it is preparing to send more soldiers to Iraq to stabilise Baghdad and, perhaps, Anbar Province.

Ms Pelosi emphasised that there was no question of cutting funds for troops already on the ground and stopped short of committing Democrats to blocking the money needed for reinforcements. Any attempt to do so would inevitably spark a constitutional clash between the President — who is US Commander-in-Chief — and Congress, which controls the military purse strings. It would also rekindle memories of Vietnam, from where the US was forced to withdraw gradually as Congress chipped away at the war budget.

Mr Bush is expected to use a nationwide TV address this week — possibly on Wednesday — to unveil his new strategy for the war in Iraq. Last week he reshuffled his military and diplomatic teams in anticipation of the announcement, which will frame the last two years of his presidency and, possibly, his legacy.

Lieutenant-General Raymond Odierno, who was appointed head of Multi-National Corps-Iraq, yesterday emphasised that the plan would be linked to economic and political initiatives. “We have always tended to look for a military solution, but it is much bigger than that,” he told reporters at Camp Victory, the US military headquarters near Baghdad. “The military plays a large role but there are a lot of other things that have to be done and I think everybody recognises that.”

Asked by The Times what he proposed to do differently following previous failed plans over three years to tackle the combined al-Qaeda, Baathist and Shia militia threats, he said: “I will tell you what we have to do and it starts with protect[ing] the population. The second thing is you have got to have a stimulation of jobs. We have to have a very focused programme of investment.”

General Odierno confirmed that these plans were among the proposals put to the Pentagon recently. “Some included surge of troops, some included a surge in economic capabilities.” Others, he said, included boosting other Iraqi capabilities in fields such as the Treasury, justice and rule of law.

There remains considerable doubt about the speed with which the overstretched US military could increase troop numbers in Iraq. It is understood that about 4,000 extra troops could be deployed swiftly while a further 5,000 from the US Army and Marines could arrive by next month. Officials say that a deployment of 20,000 additional troops, which would mean remobilising reserves, would not be completed before the spring.

Challenged on whether it was too late for more troops to make a difference, General Odierno bridled, saying: “If we think we have a new strategy it is never too late. It goes back to patience. Over time we can accomplish the mission. Now, that time may be two or three years from now, so the issue becomes: are we willing to wait two to three years or do we want to speed it up?”

The White House believes that it has secured backing for the plan from Nouri al-Maliki, the Iraqi Prime Minister, but members of the Shia-led Government remain sceptical.

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