The occasion was the party's bi-annual Southern Leadership Conference in Memphis, Tennessee. Normally, such gatherings are a relaxed opportunity for regional notables to catch up with old friends and ponder the political runes.
This one, however, was different: an anxious stocktaking ahead of the mid-term elections in November - when the party could lose the Senate, the House or both - and an early exhibition canter for many obvious contenders for the nomination in 2008.
A straw poll of attendees organised by Hotline, apolitical newsletter, was won, unsurprisingly, by the host-state's senior senator, Bill Frist, who steps down as majority leader in January ahead of an almost certain White House run.
Mr Frist won 37 per cent of the 1,427 votes. Perhaps more intriguing, however, was the second place finish of Mitt Romney, the Governor of Massachusetts, ahead of George Allen, Virginia's affable junior senator who was widely fancied for 2008.
John McCain, the Arizona senator, neatly sidestepped what would have been certain defeat by urging his supporters to vote for Mr Bush - arguing that the most important thing for the party was to unite behind the President to make a success of his remaining time in the White House, rather than abandoning him to bolster their chances of survival in the congressional elections this autumn.
But that is surely wishful thinking. After years of subservience to the White House, congressional Republicans are going their own way, as demonstrated last week by the unprecedented rebellion over the Dubai ports deal.
One reason is resentment of what they see as the disdainful treatment of Congress by the Bush administration. More important however, is the string of political miscues, culminating in the ports debacle, that has driven the President's approval ratings to new lows.
In Memphis, leading Republicans took issue with Mr Bush. Mr Romney, for example, earned ringing applause for his criticism of runaway public spending and massive budget deficits, while Mr Allen demanded tough immigration controls, in contrast to the effective amnesty for many illegal immigrants proposed by the President.
Others urged Mr Bush to shake up his White House staff, much as Ronald Reagan did in his second term, rescuing it from the disaster of the Iran-Contra scandal. "There is some question whether those around [Mr Bush] have served him well," said Norm Coleman, a senator from Minnesota.
Particular targets for criticism were Andrew Card, the White House chief of staff since 2001, and Karl Rove, Mr Bush's top political adviser and architect of his two winning Presidential campaigns. Many believe Mr Rove has been distracted by his entanglement in the CIA leak affair.
Underlying everything however is Iraq.
At Saturday evening's annual Gridiron dinner - an event that passes for Washington letting its hair down when reporters and politicians mingle amid jokes and spoofs - the President tried to make light of the difficulties of his administration.
"Dick, I've got an approval rating of 38 per cent, and you shoot the only trial lawyer in the country who likes me," he said of Vice-President Cheney's quail hunting mishap last month.
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