Two terms are more than enough. The Executive branch of our federal government has usurped enormous power unto itself never envisioned by the Founders.
Oh, they envisioned it alright. And not in a good way. Members of the Continental Congress highly influenced, or even authored term limits in their own state constitutions. Many of those constitutions contain verbatim wording from the proposals for the Articles of Confederation (which did, in fact, have term limits explicitly spelled out). Thomas Jefferson famously wrote in urging a limitation of tenure in Congress,
"to prevent every danger which might arise to American freedom by continuing too long in office the members of the Continental Congress." He had similar statements regarding the presidency.
Both Jefferson and George Mason advised limits on reelection to the Senate and to the Presidency, because said Mason,
"nothing is so essential to the preservation of a Republican government as a periodic rotation."
Richard Henry Lee of Virginia, who famously made the motion in the Second Continental Congress calling for Independence from Great Britain, and the one who's famous resolution led directly to the Declaration of Independence, viewed the absence of legal limits to tenure, together with certain other features of the Constitution, as
"most highly and dangerously oligarchic."
Mercy Otis Warren, while not exactly a Founding Father, was very connected politically, was good friends with the likes of Martha Washington, Abigail Adams and Hannah Winthrop, and was an advisor to many of the Founding Fathers, including Samuel Adams, John Winthrop, John Hancock, Patrick Henry, Thomas Jefferson, George Washington and most especially John Adams to whom she became his literary mentor leading up to the Revolution. She wrote in multiple letters to to the Founding Fathers and to others that if,
"there is no provision for a rotation, nor anything to prevent the perpetuity of office in the same hands for life; which by a little well-timed bribery, will probably be done."
For various reasons the language of specifics of term limits for the President and Congress that was in the articles of Confederation didn't make it into the US Constitution. One of the major reasons was that the nearly-universal support from the grassroots on up for the principle of rotation rendered such specifics unnecessary. The manner in which Senators get elected made the assumption that support for such rotation would remain. Senators were created in two-year classes. When the Founding Fathers agreed on six-year terms to Senators, they also decided to stagger the elections, so that a third of the Senate was up for election every two years. With this staggered rotation, the Founding Fathers wanted to ensure stability in the Senate, and to encourage Senators to deliberate measures over time rather than risk a rapid turnover of the entire chamber every six years. At the same time, they wanted more frequent elections, as opposed to waiting every six years, to prevent Senators from permanently combining for "sinister purposes". Thus two-year classes ensured a stable Senate, but also mean the Senate would turnover every 6 years (not realizing that some Senators would even want to run, much less get elected, in perpetuity).
Our Federal government, especially the Executive branch, needs to be made humble in a hurry; lest, we wake one day to find the Executive unanswerable to the people and beyond recall.
That's exactly what some of the Founding Fathers, and others, feared. Contrary to popular belief, Thomas Jefferson played no hands-on role in the composition of the US Constitution. When it was being drafted in 1787, he was 3000 miles away in France. He first wrote his details of what he liked and disliked about the new Constitution in December 1787 in a letter to George Mason, and of all of the the things he didn't like, the most disturbing to him was
"the abandonment in every instance of the necessity of rotation in office." History and experience had convinced him that, without term limits, every elected official will be
"an officer for life." The Constitution's neglect of this problem was for him a fatal flaw that would someday be the undoing of the nation.