How did George Washington's precedent of two four-year terms become so strictly adopted

This precedent was never that strict, and it's arguable that Washington is the one who set it. I have written in this sub before on the particular topic of Washington declining a third term. The bullet points are: Washington never really expressed a view that a president shouldn't serve more than two terms, as long as he was being re-elected. He only declined for personal reasons, because he was sick of the politics. He had to be convinced by Hamilton and Madison to even run for the second term. There were efforts to get him to stay on for a third but he declined. When Adams' presidency didn't go so well, there were further efforts to draft Washington for a third term in 1800. Washington declined, citing declining health, not any opposition to a president serving longer than eight years. It became moot anyway since Washington died the year before that election.

As argued in the paper "Presidential Terms and Tenure: Perspectives and Proposals for Change" prepared for the Congressional Research Service, and supported by Michael J. Korzi in his book Presidential Term Limits in American History: Power, Principles, and Politics, the two-term tradition is really more appropriately attributed to Thomas Jefferson. He had long spoken out against monarchy and the Federalists' perceived monarchist inclinations. On December 10, 1807, Jefferson wrote a letter to the legislature of Vermont in which he gave his reason for declining a run for a third term:

"If some termination to the services of the Chief Magistrate be not fixed by the Constitution, or supplied by practice, his office, nominally four years, will in fact become for life, and history shows how easily that degenerates into an inheritance. Believing that a representative Government responsible at short periods is that which produces the greatest sum of happiness to mankind, I feel it a duty to do no act which shall essentially impair that principle, and I should unwillingly be the person who, disregarding the sound precedent set by an illustrious predecessor [George Washington], should furnish the first example of prolongation beyond the second term of office."

In other words, two terms is enough for any president, since anything more could "degenerate into an inheritance", such as a monarchy.

The only other president who can really unequivocally be pointed to as following the Jefferson model is James Monroe. As Korzi points out, James Madison had argued against presidential term limits during the Constitutional Convention. In the lead-up to the 1816 election, Madison received a letter from George Joy, an ally of the Madison administration in London who had helped spread some propaganda during the War of 1812. In the letter, Joy encouraged a third run and assumed Madison didn't believe in term limits:

The motives with Genl: Washington & with Mr: Jefferson for retiring from public Life, do not, I trust, exist with you. You have had your Share of bodily infirmities; and are not so far advanced in years. I see not the least necessity for establishing 8 Years as a precedent; with the advantages of Experience, and faculties unimpaired, you may render services to the Country in its actual situation which can hardly be looked for from another; but above all it is necessary that the enemies of the Country should be undeceived with respect to the weight and power of our domestic dissentions.

Unfortunately, Madison's reply was not preserved (Madison kept his letters, but Joy didn't - there were more than 100 letters between the two men, but mostly from Joy to Madison). And Madison nor anybody else seemed to ever write on the subject again. It's unknown if Madison was following Jefferson's example, being a Jeffersonian himself and representing the Jeffersonian party. He very possibly was following Washington's example, that he was simply sick of the politics.

To that point, I think it's at least arguable that Madison may not have actually received his party's nomination or won a third term if he'd run. The Democratic-Republicans had been the political beneficiaries of the War of 1812, but Madison's handling of it wasn't particularly praised. With Secretary of State (and, briefly, War) James Monroe waiting in the wings, the party may have gone with him anyway. Since there is silence in the historical record on the subject, it's not out of line to consider the possibility that Madison believed a third term may have met with resistance in his own party, as well as with the electorate at large. Rather than suffer the embarrassment of losing the nomination, he willingly passed the torch.

As mentioned earlier, Monroe is the only president after Jefferson to really decline a third term out of an actual expressed principle that presidents should be held to two terms, no matter the political circumstances.

Andrew Jackson is an interesting case because he was in favor of term limits - but not two terms. He was in favor of one. In most of his Annual Messages To Congress, as well as in various other speeches, he advocated for a Constitutional Amendment limiting the Presidency to a single term of either 4 or 6 years (incidentally, this is the basis for the Confederacy in their 1861 Constitution of limiting their presidency to a single 6-year term). However, Jackson defied his own advocacy and ran for a second term.

Early in his second term, there were already rumors he might run for a third term under certain circumstances. In the lead-up to the 1836 presidential contest, there were some efforts to get him to run again (source 1, source 2). In early 1836, Jackson's former Vice President-turned-political rival John C. Calhoun wrote of hearing the rumor that Jackson was considering a third term if a war with France was imminent, and he suspected Jackson of orchestrating such a war just for that purpose:

"I now hold it certain that Genl Jackson is bent on a French war. He said to a lady a few days since, as I understand, that nothing could induce him to take a third term, but a war with France, and his desire to retain power is the only satisfactory explanation that can be offered for the course he has pursued."

Of course, Jackson did not pursue a third term and his declining health is often cited as the reason. Considering his willingness to break his own standard of a one-term presidency and serve two terms, it has been argued that Jackson's motivations for declining a third term were more in line with Washington's than Jefferson's. Like Washington, Jackson hand-picked his successor, which probably made the decision easier.

I have written on third term bids by later presidents here. The next president who actually could run for a third term was Ulysses S. Grant, and he did, in 1880, but lost at the Republican National Convention.

The next after him was Grover Cleveland. There was speculation in 1896 of him running for a third term, but much of the Democrat-affiliated press discouraged the idea (particularly Charles Anderson Dana, publisher of the New York Sun). Cleveland had already run three times, but his second term was marked by a severe economic downturn ("the Panic of 1893") which widened a split between the conservative Bourbon Democrats that Cleveland represented and the more progressive Silver Democrats. In the end, Cleveland didn't run and the Silvers took the nomination with William Jennings Bryan at a contentious convention.

The next president eligible for a third term was Theodore Roosevelt. He at first spoke out against them, and then changed his mind, running for a third term in 1912.

The next was Woodrow Wilson. He suffered a stroke during his second term and was widely unpopular during the end of his presidency; the Democrats lost in 1920 by the widest popular vote margin, percentage-wise, since the states started holding popular elections. During his initial 1912 campaign, when he was running against Theodore Roosevelt's third bid, Wilson was asked his opinion on third terms. His view was that presidents shouldn't run for third terms, but that it should be up to the people to decide through an election, not through a Constitutional amendment. As Korzi writes, even after Wilson's stroke, there was some continued support within the party for a third term, and Wilson appeared open to the idea, but political opponents leaked information about his health issues. Wilson then made a public declaration he would not run again in 1920.

cont'd...