A Missouri senator who held the post of President pro tempore of the Senate, David Rice Atchison happened to be the first in line of succession to President James Knox Polk (owing to the resignation of vice president George Dallas).
An argument is made that Senator Atchison held the office of President between the Polk and Taylor administrations. This argument rests on the fact that President Taylor, for religious reasons, refused to swear the oath of presidential office on a Sunday. So he delayed his scheduled inauguration until the next day, and took the oath on Monday, the fifth of March, 1849.
Some claim that during the day's delay, Senator Atchison held the office of President. The story is made all the more irresistible by the apparent fact that "President" Atchison slept through his entire "term in office" either out of fatigue or as a result of the after-effects of the Saturday night inaugural parties.
Whether Atchison was actually President makes for an interesting discussion. And, never one to short-change you, here is that discussion.
The legal truth is that Zachary Taylor became President at noon, Sunday, March 4, 1849 -- the moment that President Polk's term expired. This was specified on Taylor's writ of election as issued by the Senate when the electoral votes were counted. According to that writ of election, Taylor and only Taylor was President as of noon on Sunday. The fact that Taylor didn't take the oath until the next day has nothing to do with the fact that he was already President under the law. The oath doesn't make someone President, it only enables the President to discharge the powers of the office. Taylor was President, but until he took the oath, he couldn't perform any duties of the office, like signing bills into law, referring treaties and executive appointments to the Senate, commanding the military, etc. (and, of course, he didn't).
Those who claim a Presidency for Senator Atchison on the grounds that it takes the completion of the oath to assume the office (though this is clearly wrong) would then have to identify someone who "was President" between each and every true President; someone who was entitled to the office from the instant of noon, when a sitting President's term expires until that moment at one or two minutes after noon when the new President completes the uttering of his oath at his inauguration.
Another point to consider when thinking about the possibility of an Atchison presidency, one based on the fact that Taylor had not taken the oath yet, is the equally acknowledged fact that Senator Atchison himself never took the oath either. So it would seem that he too was unable to discharge the office of the President. (So those who claim the oath of Presidential office begins a Presidency would be hard-pressed to claim one for Atchison!)
So to give Atchison a Presidency, it is necessary to acknowledge that the oath is not the requisite act that begins a term of office. The only things that do confer the office (not the powers) of the president are the death, incapacity, or resignation of an incumbent, and the expiration of his term. In the last case, the office devolves, per writ of election, on the person certified by the Senate as having carried the electoral college. In the other cases, it devolves to a subordinate official (vice-president, etc.) immediately.
Therefore, if Atchison held the office of President, he had to have done so by reason of the death, incapacity, or resignation of an incumbent. Polk was incumbent until noon on Sunday, at which point Taylor became incumbent, so death is ruled out. Incapacity and resignation may be another story, however. Let's take resignation first.
Recently, I happened on something that said that Atchison's day in office was not Sunday, but Saturday, the day before the scheduled inauguration! If that information is true, then this could indeed qualify Atchison as having held the office of President (but not its powers). Under this information, President Polk actually formally resigned the Presidency, effective Saturday, so that he could get out of town early, so anxious was he to return to Tennessee (a big mistake as it turned out, because he rode right into the cholera epidemic that killed him a month later).
If Polk did indeed resign, the office of President would have devolved onto Senator Atchison as next in line of succession, and Atchison would indeed have been President. He would have been eligible to take the oath of Presidential office and thereupon assume the powers of the office (again, the fact that he never did would not mean that he was not President).
Now for an argument that Atchison (or someone else!) held the office between Polk and Taylor by virtue of incapacity of the office holder! If we assume that Polk served out his term (that is, he did not resign early), we can fairly ask, "who could have taken the oath of presidential office on Sunday?" Obviously, Taylor (who held the office by authority of his writ of election) could have. But perhaps Atchison could have done so too! In theory, the President (Taylor) was in a position of "incapacity" -- he was incapable of exercising his Presidential powers simply by virtue of the fact that he had not taken the oath to assume those powers to himself yet!
Atchison could perhaps have argued that he was entitled to claim and exercise the powers of the presidency, by saying that the office had actually become his at the very stroke of noon by virtue of the incumbent's "incapacity." By all rights, he could claim to be entitled to hold the office of the president (and the right to exercise its powers, if he himself took the oath) until the moment that Taylor swore the oath, thus removing his "incapacity" to govern.
Could someone other than Taylor and Atchison have argued a right to the office? By custom, an incoming vice-president is sworn into office before his president. So maybe Atchison's "window of opportunity" for this little power-grab was shorter than 24 hours. As soon as Millard Fillmore removed his own incapacity by swearing the oath that gave him the powers of the vice-presidency, he (not Atchison) became next in line of succession to the incumbent chief executive (Taylor).
It is interesting to think about a successful vice-presidential candidate who is sworn into office on inaugural day, and then, instead of leading the Senate outside to attend the inaugural of the president, demand that he be immediately given the oath of Presidential office by reason of the incumbent's incapacity to exercise his powers! This usurper would then (in this work of fiction) immediately issue an executive order that somehow prevents the inauguration of his running-mate!
This is getting to flights of fancy more suited to discussion in novels rather than on these pages. In point of fact, even if this "incapacity" argument has merit, then there are theoretically two men who could take the oath of office after the expiration of any and every presidential term. Two men that could both make a claim to the office; one by writ of election, and one by a perhaps contrived application of the incapacity clause, claiming that the other is not (yet) capable of exercising presidential powers. It is infeasible, though, for history to record both these men as Presidents. Only the one who eventually does take the oath should be counted. Even if Atchison had this "incapacity" argument, he didn't use it, and therefore, this lets Atchison out in my book, since he was no more entitled to the office of President than was Taylor.
So my view is that if Polk did indeed resign his office, Atchison did hold the office of the Presidency (but without the right to exercise its powers -- he never took the oath). But if Polk did not resign, and I have yet to see concrete evidence of a formal resignation, then his term expired as normal at noon on the fourth of March, at which time Zachary Taylor became President by the authority of his writ of election. His choice not to exercise any Presidential powers -- nor even to give himself the authority to do so -- until the next day, is inconsequential.
I have always been under the (perhaps mistaken) impression that the concept of an Atchison presidency was not contemporaneous with the senator himself. I had understood that this concept grew up long after he was dead and that he himself never considered himself the holder of the office between Polk and Taylor's term. The myth of his Presidency is engraved on a plaque of more recent vintage at his gravesite.
Note: this exposition and reasoning is original with me, and I stand by it even if you can't find any respected historians who agree with it (to be honest, I haven't looked, but I would be surprised if I am the only one who sees the Atchison "presidency" this way).