What popular vote in 1800?
Problem was that there was no popular vote in 1804, or even 1796! If you look at the elections, the popular only started to be recorded in 1824! So what argument since most states electors were chosen by state legislatures before 1828, so nobody would think to institute popular vote in 1800, 1804, just like in 1789.
Many states chose electors (pledged to a particular candidate) by popular vote (either statewide or by district) before 1824, and it is a myth that the popular vote before that time is unknown. Scholars have been able to reconstruct it fairly well, using old newspapers and other sources. An excellent source is "A New Nation Votes: American Election Returns 1787-1825"
https://elections.lib.tufts.edu/about.html For example, here are the 1812 returns for Pennsylvania:
http://staffweb.wilkes.edu/harold.cox/pres/PaPres1812.html
The basic problem with a national popular vote before the ACW was slavery. Indeed, the Electoral College was chosen largely because it was the closest you get to national popular vote without putting the South at a disadvantage. To quote an old post of mine:
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A fact that is insufficiently recognized is that at the Constitutional Convention, the big issue in electing the president was *not* between direct popular vote and the Electoral College, but between popular vote (whether directly or through an electoral college ) and election by Congress. The obvious problem with direct popular election is that it would put the southern states at a disadvantage--even one as large as Virginia, for as Hugh Williamson of North Carolina remarked, "Her slaves will have no suffrage."
http://books.google.com/books?id=n0oWAAAAYAAJ&pg=PA32
One might think that the advocates of legislative election based their arguments on the idea that the legislature should be supreme, but that was not really the case. The delegates quickly decided that the president should be independent of the legislature, but almost until the end of the Convention the small states still favored legislative election, which they felt would be more beneficial to their states and, as Williamson argued, not inconsistent with executive independence, given a fixed salary for the president and no possibility of re-election. What was ultimately decided on was a compromise satisfactory to the legislative-election advocates, not only because the Electoral College was based on legislative apportionment--with the resulting advantage to the small states, especially thanks to the two electoral votes each state got for its Senate representation--but also because it was widely assumed that in most elections, no candidate would get a majority, and the race would go into the House, to be decided on a one-delegation, one-vote basis.
Contrary to the widespread belief that the Electoral College was meant as an "elitist" anti-democratic measure, the most avid supporters of the Electoral College were the advocates of popular election. They felt that the Electoral College was the closest one could get to a popular-election plan that could actually pass the Convention, given that small states had the balance of power there, and given the practical difficulties posed by differences in electoral laws and conditions from state to state--and especially the obvious difficulty pointed out by Williamson on how direct elections would limit the power of the slave states. James Wilson who as early as June 1 had called for popular election of the president, on June 2 called for election by electors chosen by the people, "but this was not meant as a significant change and was never really considered as such by the leading members of the Convention. The major alternatives were legislative election versus some form of popular election, either direct or indirect..." David K. Nichols, *The Myth of the Modern Presidency,* p. 40.
http://books.google.com/books?id=x6qPrM4B32IC&pg=PA40
Nichols notes that "It is also commonly assumed that the use of electors was a product of the Framers' distrust of popular opinion. In support of this claim we are often treated to quotations from delegates to the convention such as George Mason who said 'It would be as unnatural to refer the choice of a proper character for chief Magistrate to the people, as it would be to refer a trial of colours to a blind man.' There is, however, a major problem with using such statements to show the antidemocratic character of the electoral college. The delegates who expressed the deepest distrust of popular votes were delegates who eventually opposed the Constitution, such as George Mason or Elbridge Gerry, or those who favored election by the legislature, such as Roger Sherman, Charles Pinkney, or George Mason...
""But what of Alexander Hamilton's argument in the *Federalist*? There Hamilton claimed that the electoral college would refine popular opinion, would prevent the worst aspects of popular opinion from operating in the election of the President. Some delegates probably supported the electoral college because they saw it as a check on popular opinion. But it is interesting to note that Hamilton's argument in the *Federalist* for the refining effect of the electoral college was not made at the Constitutional Convention. Instead, Gouverneur Morris argued that the extent of the nation would serve to refine popular choice. Morris contended that although persons of dubious character and ability might be elevated to office in a single district or state, they would be unlikely to be elected by the nation as a whole. Only worthy candidates would have a chance of gaining election from so large a constituency. For Morris it was the size of the nation, and not the judgment of the electors, that would screen unworthy candidates. Hamilton borrows Morris's language for use in the *Federalist* but he substantially alters Morris's argument..."
http://books.google.com/books?id=x6qPrM4B32IC&pg=PA43
Morris, as it turns out, was more perceptive than Hamilton (or than many small-state delegates who wishfully thought that presidential races would frequently be thrown into the House; Morris correctly predicted that this would not be the case, arguing that under the new constitution with its more powerful national government, men with national reputations would be likely to arise, and people would vote for them rather than waste their votes on local or regional favorites). The Electoral College never really "screened" public opinion; the party system did that. Even as early as 1796, the first "faithless elector" provoked howls of outrage ("What, do I choose Samuel Miles to determine for me whether John Adams or Thomas Jefferson shall be President? No! I choose him to act, not to think.") and even further back, in 1792, when the presidency was uncontested, the vice-presidency was basically determined on party lines, with electors voting for Adams or Clinton based on which party had the support of the voters or legislatures that chose the electors. In short, from a *very* early time, the Electoral College became an essentially popular election (admittedly in a modified form), and arguably was intended as such from the beginning.
In fact, even the Anti-Federalists conceded the popular nature of the Presidency. To some, that was part of the problem. Patrick Henry said, "To me it appears that there is no check in that Government. The President, Senators, and Representatives all immediately, or mediately, are the choice of the people."
http://press-pubs.uchicago.edu/founders/documents/v1ch11s13.html