PART I
It was. There just was too much squabbling to get something through, something that had often been a problem since quite literally 1789.
Let's start in 1813. That summer, the 62 year old James Madison had a genuinely nasty illness - there were multiple reports he might not survive, and a young Daniel Webster visited and found he was barely coherent - followed by putting himself at risk during the second year of the War of 1812, followed by his 70 year old Vice President Elbridge Gerry (whose manipulation of congressional districts lives on in the term 'gerrymander') actually dying in 1814. Gerry had been seriously ill on and off even before Madison was, so at the time Madison was sick, there was widespread speculation that both the President and Vice President might die at the same time.
The governing law at the time in such dire circumstances was the 1792 Presidential Succession Act. That had come to pass after the First Congress got so caught up in arguing about if the Constitution had already mandated the President Pro Tempore of the Senate and Speaker of the House as the "Officer" described in the Succession Clause that it failed to pass anything. As strange as it sounds nowadays, a substantial amount of debate also revolved around whether the Chief Justice should really be the rightful third in line.
The next Congress then first got sidetracked over the possibility that anyone assuming executive office this way might potentially hold two offices simultaneously (along with the even more horrible thought they might draw two salaries and/or be biased by the potential of voting on salary increases - there's a reason the 27th Amendment regulating Congressional pay raises came out of that time period.) It then got engaged in a nasty proto-partisan battle because Jeffersonians thought that their beloved Secretary of State should be first in line after the Vice President and had the votes in the House to attempt to do so. Hamilton, however, was unsurprisingly deathly opposed to this possibility, and the proto-Federalists in the Senate blocked it and eventually forced Pro Tem first, Speaker second - and also mandated that if one of them had indeed succeeded, their term of office would be at most 17 months as a special election for President and Vice President would take place.
So with that, Congress in 1813 thought for a time that they might have one of their own be the next President. Except...on top of everything else, Madison had sent off the then-President Pro Tem, William Crawford as Minister to France. (The Minister jobs to France and the United Kingdom were the two highest salaried positions in government after the Presidency at the time, and Crawford already had enough clout that he was widely considered to be the likely front runner in 1824 until he had a stroke; American political history might have been very different if he'd stayed healthy.) So this set off a feeding frenzy in Congress, which even more unusually was in session at the time because of the war. Monroe wrote that half the Senate was trying to maneuver into becoming Pro Tem, and in the House, Speaker Henry Clay was implied by opposition press to be waiting eagerly for Gerry to die. Fortunately, by the time he did Madison had recovered and lived another two decades.
Then another issue arose. In 1841, when William Henry Harrison became the first President to die in office, nobody quite knew what to do with John Tyler. Was he President? Vice President with the powers of the Presidency? Acting President? John Quincy Adams thought the second, several Congressional leaders thought the third, but in one of the few good decisions a generally awful President made, Tyler took steps to do everything he could legally to confirm the first option, including taking a specific oath as such and getting a joint resolution through Congress to establish the precedent - but there was still no law to confirm any of this, even after two other Vice Presidents had accessed.
Then in 1881, James Garfield was shot by a patronage seeking madman (he thought he was deserving of the Minister to France job given he'd written a couple of Unabomber-style pamphlets no one read) and thanks to medical treatments that should have gotten his incompetent physician shot himself, spent three months slowly dying at a beach house. Nobody really had thought about temporary incapacitation before this, with the additional problem of Vice President "Good God!" Chester A. Arthur being widely (and up to that point, quite properly) perceived as the tool of Roscoe Conkling, the corrupt political boss who was at the time the king of patronage. While he'd obviously had nothing to do with the shooting, it was pretty obvious that if and when Garfield died, Arthur succeeding and Conkling ascending was exactly what the assassin wanted.
So Arthur took massive pains to avoid doing anything resembling the execution of Presidential power while Garfield lingered over fears that he might be viewed as usurping his office, and the government was even more rudderless for those three months than when Woodrow Wilson had his stroke nearly 40 years later. Even worse, the House had no Speaker as it wasn't scheduled to convene until December 1881 (and while the previous Speaker's term had in any case expired in March, it had also switched from Democratic to Republican control.) The Senate in turn had briefly convened in special session after the election to confirm Garfield's Cabinet, but with the elections providing the first ever 50/50 split between Democrats and Republicans, it got nowhere close to electing a Pro Tem and punted it to the next regular session in December. So no Speaker, no Pro Tem, Congress not in session - and only the President had the constitutional authority to summon it back before December.
When Garfield died in September, this was as close to as an outright governmental decapitation scenario as the United States has ever faced. Arthur, who was in New York traveling to Washington with Garfield's body, wisely and immediately wrote up a proclamation to summon the Senate into special session and had it special delivered to the White House just in case something happened to him on the trip; when he got there, he destroyed it and summoned it himself in October. This was when the Senate was fortunate to have David Davis, a close friend of Lincoln, as while he was nominally a Republican he was also viewed as relatively non-partisan and the one person both parties could agree on to serve as Pro Tem. (Davis also was supposed to be the independent Supreme Court nominee to the 1877 commission that decided the Hayes-Tilden dispute, but in a dumb move by Democrats, he'd been offered a Senate seat as inducement for his vote - except he took it immediately and dropped off the commission.)
But I think you may be starting to see some of the problems. In 1881, the United States was still operating under a 1792 law that predated not only the Twelfth Amendment but had been designed when the modern political system still hadn't even been anticipated. Moreover, one of the reasons that Andrew Johnson wasn't convicted was because a number of Republicans were vigorously opposed to Ben Wade, the Pro Tem at the time, from becoming President - partially because he might interfere or outright successfully fight Grant for the nomination, and partially because his policies were anathema to many. (A number of large bribes also helped too.) So 80 years later, no progress had been made despite multiple demonstrations of just how close the United States had come to disaster.
Edit: US didn't send Ambassadors until the 1890s, so their actual title was "Minister".
PART II (went over the 10K limit, so borrowing from this post!)
So after the near disaster, Congress in 1883 finally acts...to pass the Pendleton Civil Service Act. In fairness, this was not an entirely insignificant achievement as despite decades of calls for reform, doing something theoretically meaningful about patronage had long been thought politically impossible until Garfield's assassination, especially since kickbacks from job holders had provided the majority of funding for political parties more or less since they began. Unfortunately, the reforms ended up proving more of a veneer than anything else, but on the bright side Chester Arthur shocked everyone and gained a backbone partially thanks to a remarkable set of correspondence from the housebound Julia Sand, broke with Conkling and most of Garfield's cabinet, and governed as cleanly as could be expected.
However, this gives an idea of the historic priority given to changing the law; if the President were seemingly healthy and young no one gave much thought to it. Near term partisanship also kept cropping up too; one 1856 attempt took inspiration from 1789 when it suggested that the Supreme Court provide the next set of candidates for the line of succession, starting with the Chief Justice and then proceeding through the Associates by order of seniority. That the Chief Justice was Roger Taney and Dred Scott had just been decided implies there may have been just a little bit of politics involved, especially since the proposal came out of the Southern-dominated Senate and went precisely nowhere, similar to several other reform attempts made over the years.
Instead of my typical novels, I'm going to just add one brief clarification to some fine folks here mentioning Eisenhower.
Eisenhower suffered a significant heart attack in September 1955, and was also hospitalised and required surgery due to his ileitis in June 1956. Compounding these health concerns, he also suffered a stroke on November 27, 1957.
Eisenhower (and Dulles, given his uncle's experience with a presidential stroke) was incredibly concerned about both being incapacitated again, or, in his mind worse - being "coherent" but unfit for responsibly carrying out the duties and requirements of the presidency.
The work around he implemented in many ways became something of an inspiration point (though not really a template) for the 25th Amendment.
He wrote Nixon a letter, and then made that letter available to his cabinet after Nixon had read it. I'm going to simply quote my dissertation, but it includes the relevant reference.
"The letter granted Nixon a rather staggering power in that while he requested Nixon consult the Secretary of State and others before removing him from office, Eisenhower granted Nixon sole power to make that decision." See Letter, Eisenhower to Nixon, February 5, 1958, 1958, Feb. 5, Box 11, Special Files – Dwight D. Eisenhower 1957-1966, RNPPM, RNL; Nixon, RN, 227-228).
The letter outlined that Nixon, and really Nixon alone (as Vice President) had the responsibility and power to decide if Eisenhower was incapable of carrying out his duties. There is every reason to believe that Eisenhower thought he might have another stroke while in office - he complained to Nixon about exactly that possibility - his first stroke left him with a speech impediment (only those closest to him could notice it after his recovery) and this caused him a great deal of frustration and agitation; for a man with an already famous temper and who believed stress and anger would lead to another stroke, this meant Eisenhower thought a second stroke was inevitable (he died not of a second stroke, but of heart failure).