Let's start with this map, which colors each state, D.C., and each congressional district in Maine and Nebraska in varying shades of green based on how well Gary Johnson performed there in 2012. 8 jurdisictions (state, district, congressional district) are assigned to each shade from 30% to 90%. The darker the shade, the more libertarian the state is, and the likelier it is to be won by a libertarian candidate:
Obviously, this map isn't perfect, as it overestimates NM (Johnson's Home State), and underestimates MI (where Johnson was only a write-in candidate) and OK (where you couldn't even vote for Johnson), but it's still pretty good.
The next three maps show different scenarios for the libertarian, and are meant to show how their electoral map would grow as their support gets higher and higher.
In each map, states the libertarian wins are shown in
blue, using the exact same margin shading they had on the first map.
The states the libertarian
DOES NOT win are colored in the exact same shade of
green they were colored in on the first map.
Scenario 1 - "We finally won some electoral votes!" (Libertarian wins only the states that had 90% shading on the first map):
Libertarian Electoral Votes - 37
Scenario 2 - "The Libertarian Support Rises Some More" (Libertarian wins the jursdictions that had 80% or 90% shading on the first map)
Libertarian Electoral Votes - 73
Scenario 3 - "The Probable Libertarian Peak" (Libertarian wins the jursidictions that had 60%, 70%, 80%, or 90% shading on the first map)
Libertarian Electoral Votes - 265
As you can see, getting a libertarian into the white house is VERY difficult. To do it, the libertarian would not only have to
run the table with the 60%, 70%, 80%, and 90% jurisdictions, but would also have to win in NC (which was Johnson's best state among the states in the 50% shading). Perhaps a better goal would be to throw the election into the U.S. Congress.
Here's a hypothetical election being thrown into the U.S. Congress, with the libertarian achieving the minimum performance needed to do this. (all of the 70%, 80%, and 90% jurisdictions, plus Johnson's "best half" of the 60% states) and all other states voting as they did in 2012. Red is Democrat, Blue is Republican, Green is Libertarian. (note that this map does not attempt to make predictions on the margin each state will be carried by):
Democrat - 268
Libertarian - 154
Republican - 116
Note: While this is the minimum libertarian performance under a uniform swing system, if you take away the 'uniform swing constraint', you can give all the green romney 2012 states back to the republicans and still get an election being thrown into the U.S. Congress.
So, in Conclusion, even if the libertarians do have a major boost, getting them to the white house is still very difficult, and even throwing the election into the united states congress would be a significant accomplishment, unless Republicans are improving their electoral performance at the same time.