Laura Bush held an early family party for him on Wednesday, to which a few professional golfers were also invited, and on Thursday the president made a rare outing to watch a baseball game. But these few birthday celebrations apart, it has been a relentless week for the US president.

A backlash against his decision on Monday to commute the jail sentence of the former White House aide Lewis "Scooter" Libby was followed on Thursday by the withdrawal of support for his Iraq strategy by Pete Domenici, a Republican senator for 35 years. The loss of such a loyal senator is ominous for Mr Bush's war plans.

More defections are expected, and Mr Bush cuts a lonely figure, holed up in the White House fretting over his legacy.

Professor Robert Dallek, author of several books about the presidency, said that while it was not unusual for a president to limp to the end of his term as a lame duck, he saw Mr Bush as a particularly pronounced case. "If you are looking at defeat, no one wants to be associated with the person responsible. This is the case with Bush. You do not see his party rally round. He has united opinion against him and it makes for a lonely, isolated position," Prof Dallek said. "Once a president loses trust, he cannot govern effectively."

Although he has 18 months left in office, Mr Bush's options are limited. Last week, he lost his last chance for snatching a lasting domestic legacy when his immigration reform bill was destroyed in Congress. On foreign policy, there is little optimism of a late breakthrough on Israel-Palestine, Iran or Iraq.

The Washington Post reported this week on academics invited to the White House to discuss with him his legacy, including Sir Alistair Horne, author of a history of the Algerian revolt, which has parallels with Iraq. They, as well as former staffers and friends, spoke of his loneliness, his agonising over how history will portray him. Michael Conaway, a still loyal senator and long-time friend, said the president appeared to be worn down by the pressure and spoke of "a marked difference in his physical appearance".

Although never a social animal, he is reluctant to drop into Washington restaurants unannounced for dinner, as the Clintons did, in part because he is fearful of the public response. This week, in particular, because of the Libby decision, he has largely avoided public contact - his July 4 speech in West Virginia was invitation-only.

The White House presented the Libby decision as a non-political compromise.

A well-connected source in Washington challenged the consensus that Mr Bush's poll ratings, at just under 30%, could not fall much further because that figure represented bedrock Republican support. The source said commuting Mr Libby's sentence, a popular move among Republicans, was a panic measure after an alarming erosion in support, mainly because of hostility to the immigration plan.

Mr Domenici's withdrawal of support followed the desertion of the Republican senator Richard Lugar last week, also over Iraq. About 50% of the sitting Republican senators face re-election in November next year and their constituents have made them well aware of how unpopular the Iraq war is.

The White House yesterday expressed disappointment, saying it had hoped the senators would not go public with their frustration before September, when the army and others report back on whether Mr Bush's "surge" strategy is working.

Steve Clemons, head of the progressive thinktank the New America Foundation, has heard the reports of Mr Bush's decline in power and is sceptical. He cautioned: "Even though he has lost some ability to dictate events, he is still capable of deploying major influence on the big issues. We went through the same thing with [Vice-president Dick] Cheney when people thought he was down and out. I think it is a big mistake to think Bush is now powerless."

With little positive to show from six years in office, Mr Bush has been talking up his transformation of the supreme court as his legacy. He has given it a strong rightwing bias, demonstrated by rulings on abortion, employment discrimination and rejection of death penalty appeals. That will please Republicans, at least.

But Prof Dallek remains unimpressed. Rating the worst presidents, he said: "Hoover was a disaster. Warren Harding rates very low in the pantheon of presidents and it is likely that Bush will be seen as a bottom feeder."