Final answer:
John Adams' service as a Vice President and later as the President saw him facing and managing various political challenges, including dealing with opposition from Thomas Jefferson's party and making strategic judiciary appointments.
Step-by-step explanation:
Sewall's proposal regarding John Adams' capacity in the administration was not explicitly mentioned in the provided reference materials. However, John Adams, having served as a Vice President under George Washington, ascended to the presidency himself in 1797. During his presidency, he addressed various challenges, such as the political opposition from Thomas Jefferson's Republican Party and the retention of Washington's advisors. Adams sought to work with Jefferson, who was of the opposition party, but ultimately became his Vice President, showing Adams' capacity to negotiate political differences and his desire for bipartisan support. Moreover, during his presidency, Adams appointed John Marshall as Chief Justice of the United States and made the 'midnight appointments' to secure a Federalist judiciary before leaving office after losing the 1800 election to Jefferson.