But other than Mr. Corker, few rushed to Mr. Tillerson’s defense in recent days, reflecting a larger disappointment with him.

Mr. Tillerson was an unconventional choice for the job in the first place. While he spent 41 years at Exxon Mobil, working his way up to chief executive of the world’s largest publicly traded oil and gas company, he was the first secretary of state in American history without prior experience in government, politics or the military, working for the nation’s first president also without such a background.

No matter how often successful business leaders like Mr. Tillerson assume they can master the public sector just as they did the private sector, government rarely submits to the will of the new master. At Exxon Mobil, Mr. Tillerson was the undisputed chief whose orders were not to be ignored and who had no need to engage the public if he chose not to. After 10 years running one of the largest companies on the planet, he was unaccustomed to the role of subordinate. And Mr. Trump does not make it easy for anyone to make that transition.

The most successful secretaries of state were those with close working relationships with their presidents, like Dean Acheson under Harry Truman, John Foster Dulles under Dwight D. Eisenhower, Henry A. Kissinger under Richard M. Nixon and Gerald R. Ford, and George P. Shultz under Ronald Reagan. Condoleezza Rice was so close to Mr. Bush that she was seen as the most influential member of the administration in his second term.

“The ideal situation is where there is a direct and close relationship with the president whereby the secretary of state is seen as the primary spokesperson of the president and the administration on foreign policy,” said Edward P. Djerejian, a longtime diplomat and director of Rice University’s Baker Institute for Public Policy. “This means the president has to empower the secretary of state in this role.”

No secretary of state was as close to his president as James A. Baker III, who had been a personal friend of the elder George Bush for decades since their days as tennis doubles partners at the Houston Country Club. “Nobody was going to get between me and my president,” Mr. Baker said repeatedly.

Other secretaries who could not reconcile themselves with their presidents did not fare as well. William Jennings Bryan quit in protest of Woodrow Wilson’s policies leading to entry in World War I, while Cyrus Vance resigned in protest of Jimmy Carter’s decision to mount what was ultimately a failed military operation to rescue American hostages in Iran. Colin L. Powell was boxed out by rivals under the younger Mr. Bush and left unhappily. John Kerry was not close to Barack Obama but ultimately won support from his president for his Iran nuclear deal.