So, I've covered how many electoral votes, or states or congressional districts carried, it would require to possibly become president or vice-president of the United States via the "bust the electoral college and send the election to Congress" path. How many individual votes would it take?
The answer is in fact indeterminate, but it's possible to generate a reasonable estimate of the minimum.
We know that a presidential candidate could kick the election into the House, and become eligible for election to the presidency, with as little as one electoral vote.
And since Maine and Nebraska apportion their electoral votes by congressional district, it would be possible to pick one of those electoral votes up with as few as 1/3 + 1 of the individual votes cast in a congressional district.
No, I am not going to go through all of those two states' congressional districts to find the one with the lowest historical turnout. I'm just going to choose Nebraska's 1st US House District, and its presidential vote totals from 2012, as a reasonable proxy.
In 2012, a total of 264,712 presidential votes were recorded in that district. In a three-way race, 88,238 votes would be 1/3 + 1.
Of course, the number could go even lower than that -- lower turnout, or more candidates in the race (in 2012 there were four in the district: Mitt Romney, Barack Obama, Gary Johnson and Randall A. Terry), or whatever.
But it seems plausible to put the minimum number of popular votes required to become president via a House election at "fewer than 100,000."
Vice-president is, again, more complex. Remember, it's going to take 135 electoral votes and a second place finish to get to possible election via the US Senate ... and we can't just assume bare pluralities in the three of the four most populous states plus one state with 13 or more electoral votes.
Why? Because electoral votes are proportionally weighted toward the smaller states. EVERY state gets AT LEAST three electoral votes (two base electors plus one per US House district).
For example, the three least populous states -- Wyoming, Vermont and Alaska, with a combined population of not quite two million -- dispose of a total of nine electoral votes, while the four states disposing of nine electoral votes each (Tennessee, Indiana, Arizona and Massachusetts) have populations in the 6.5-6.8 million range.
I suspect a Ph.D.-level mathematician or statistician could model the problem and produce a number. But I'm not a Ph.D.-level mathematician or statistician. I've reached the level of my own mathematical incompetence.