In campaign advertisements and on the stump, at least six Republicans in tough re-election battles directly contradicted a claim by the President that Mr Rumsfeld was doing a “fantastic” job. Their swift response marked the latest attempt by endangered incumbents to distance themselves from the increasingly unpopular war in Iraq and the polarising figure at the Pentagon.

Asked on Monday if he was expecting Mr Rumsfeld and Dick Cheney, the Vice-President, to remain in their jobs until he left office in January 2009, Mr Bush replied “Yes, I am”, before adding: “Both men are doing fantastic jobs and I strongly support them.”

Even though Mr Bush was responding to a direct question, the subsequent headlines were an unwelcome intrusion for Republicans in tight races.

A spokesman for Tom Kean, a Republican Senate candidate in New Jersey, told The Times: “Obviously we’re incredibly disappointed in that decision. We feel Iraq is on the verge of chaos and a new Secretary of Defence is needed if we are to change the direction and implement tactical changes.”

In addition to Mr Kean, Republican Senate candidates in Rhode Island, Maryland, Ohio and Tennessee either suggested or demanded that Mr Rumsfeld should step down. In Ohio Anne Northup, a Republican congresswoman struggling in her re-election bid, said: “I don’t want to depend on the same team, meaning Rumsfeld.”

Pressure on Mr Rumsfeld increased this week with the leak of a US military chart showing that Iraq was sliding into “chaos”. Democrats, and some retired generals, have called repeatedly for Mr Rumsfeld to resign. The new statements by Republicans show how damaging the war in Iraq has become to the party — but also what a useful lightning rod Mr Rumsfeld has become for the President, as he is the main focus of critics of the war.

Mr Rumsfeld will overtake Robert McNamara, in charge of the Pentagon during much of the Vietnam War, as the longest-serving Defence Secretary next month. Despite the comments by Mr Bush, if Mr Rumsfeld becomes too damaging to the party — or if Iraq becomes so chaotic that a senior figure has to be thrown to the wolves — there will always be a way for Mr Bush to drop him.

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