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He had a bad relation with his cabinet which he inherited from his predecessor.They all resigned in protest except for Sec. of State Daniel Webster, when he vetoed that banking bill that his party had fought to pass.
John Tyler in 1841 in a dispute over fiscal policy. Secretary of State Daniel Webster was the only member to remain in office
Thomas Jefferson resigned as Secretary of State in 1793.
The cabinet secretary resigned when evidence showed his participation in the coverup. Stranded on the remote island, the crash survivors were resigned to the possibility they might not be rescued.
Ruth Kelly stated that she resigned from the cabinet to spend more time with her family.
Daniel Webster
Off the top of my head, I can only think of one signer who became a cabinet member, and that was Thomas Jefferson, who was Secretary of State under Washington, but he resigned in 1793.
Thomas Jefferson, who was the Secretary of State in Washington's first cabinet, resigned after it seemed to him that Washington was siding with Hamilton in the disputes that Jefferson was having with Hamilton.
Several of them resigned over the eight years that Washington was president. Edmund Jennings Randolph was forced to resign as secretary of state amid charges of corruption which proved unfounded. Jefferson and Hamilton disagreed on many principles and both resigned eventually.
Tyler's refusal to carry out his own Whig party's policies
First, it should be noted that historically, cabinet members have come and gone. Some leave due to poor health or retirement, others are replaced because the president feels another person might do a better job. This administration is no exception. By some counts, at least seven members have either retired, resigned, or been replaced. These include Robert Gates, secretary of defense (retired-- replaced by Leon Panetta); John Bryson, secretary of commerce (resigned after an automobile accident; replaced by Acting Director Rebecca Blank; and Rahm Emmanuel, chief of staff (resigned to return to Chicago and run for Mayor; replaced by Jack Lew).
After he vetoed the banking bill, most of his cabinet resigned and he was expelled from his party. That made it hard for him to govern and he had no chance for a second term.