You can win with only 13.8M votes or so like this:

Let's also assume that the number of votes cast in a particular state is proportional to the population of that state. (If some states have higher turnout than others, we can engineer an even bigger gap.)

These 12 states: CA, TX, NY, FL, PA, OH, IL, GA, NC, VA, WA, and NM collectively have 269 electoral votes, and a total population of ~150M and so generate ~22.4M votes

Imagine that there are two candidates, A and B. Suppose A gets no votes at all in these 12 states.

Now, the remaining 38 states have a population of 184M and so generate ~27.6M votes. If A gets one more vote than B in these states, then A wins those electoral votes. Roughly, that means A can win 271 electoral votes by having ~13.8M voters in these states.

Overall, then, A can win the electoral college vote with only 13.8/50 = 27.6% of the popular vote.

Now there are a few obvious flaws here over and above the assumptions about number of candidates and fraction of population who votes:

* It's unlikely that A would get ZERO votes in the twelve populous states. I don't know where the 1:1,000,000 mark is, but clearly the above analysis is a best case.

* There are a few states that award their electoral votes in proportion to the fraction of the popular vote received rather than all-or-nothing. I've ignored that here.

Despite these flaws, the bottom line of the analysis is still accurate -- you can become president with considerably less than 50% of the popular vote, even without a 3rd party candidate siphoning votes away.