Can Gary Johnson win a state and force the House to pick POTUS?

A favorite theory among libertarians and #NeverTrump voters is that a victory by Libertarian Gary Johnson in one or more states could deprive both Hillary Clinton and Donald Trump from winning 270 Electoral College votes. If no one reaches 270, the election is decided by the House of Representatives from any of the top three vote-getters in the Electoral College.

To clear any confusion, here’s what it says in the Constitution’s 12th Amendment: “If no person have such majority, then from the persons having the highest numbers not exceeding three on the list of those voted for as President, the House of Representatives shall choose immediately, by ballot, the President.”

So, in theory, if Johnson wins a state, he would make the top three and could be chosen as president by the House. In particular, Johnson’s supporters think he should target his home state of New Mexico and the pro-pot state of Colorado.

If Johnson won New Mexico, the map would need to look like this (or very similar):

Basically, you can switch around a few different variations of swing states and get both candidates under 270, but it needs to be close to this scenario.