“He’s a very loyal Republican, and you won’t see him go against Bush,” said a colleague of Mr. Baker, who asked not to be identified because the study group is keeping a low profile before it formally issues recommendations. “But he feels that the yearning for some responsible way out which would not damage American interests is palpable, and the frustration level is exceedingly high.”

At 76, Mr. Baker still enjoys a reputation as one of Washington’s craftiest bureaucratic operators and as a trusted adviser of the Bush family, which has enlisted his help for some of its deepest crises, including the second President Bush’s effort to win the vote recount in Florida after the 2000 presidential election. Mr. Baker served as White House chief of staff, as well as secretary of state under the first President Bush.

Andrew H. Card Jr., President Bush’s former chief of staff, acknowledged recently that he had twice suggested that Mr. Baker would be a good replacement for Secretary of Defense Donald H. Rumsfeld. Mr. Bush rejected that advice, and some associates of Mr. Baker say they do not believe he is interested, at his age, in taking the job, which could put him in the position of having to carry out his group’s advice.

Those proposals — which he has said must be both bipartisan and unanimous — could very well give Mr. Bush some political latitude, should he decide to adopt strategies that he had once rejected, like setting deadlines for a phased withdrawal of American forces.

Given his extraordinary loyalty to the Bush family — Mr. Baker was present on Saturday at the formal christening of a new aircraft carrier named for the first President Bush — it was notable on Sunday that Mr. Baker also joined the growing number of Republicans who are trying to create some space between themselves and the White House.

On Sunday, on “This Week,” Mr. Baker was shown a video of the Republican chairman of the Senate Armed Services Committee, Senator John W. Warner of Virginia, who said last week that Iraq was “drifting sideways” and urged consideration of a “change of course” if the Iraqi government could not restore order in two or three months. The American ambassador to Iraq, Zalmay Khalilzad, has offered a similar warning to the Iraqi government.