Johnson also topped the Libertarian ticket in 2012, earning 1 percent of the vote on his way to a third-place finish. In his home state, Johnson earned 3.6 percent of the total vote, not making much of a difference in Barack Obama's 10-point margin of victory over Mitt Romney.
But Johnson's team -- and, separately, Republicans who oppose the candidacies of both Donald Trump and Hillary Clinton -- clearly hope that this year will be different.
The sputtering push for a third-party candidate to challenge Trump and Clinton has a few strikes against it before it enters the batters' box. For one thing, an effort to run an independent candidate across the country has already missed key signature-gathering deadlines, necessitating legal action to get on the ballot. For another, there's little consensus on who that candidate should be.
The Johnson-Weld ticket avoids both of those problems. The candidates are all-but-set (the convention is later this month), and the party is set to already be on the ballot in all 50 states. But the ticket also accomplishes another goal of the third-party effort: It could shift the vote in some states that otherwise might be easy wins for Hillary Clinton.
If the goal is preventing either Trump or Clinton from being inaugurated in 2017, the only real option is keeping Trump or Clinton from getting a majority of electoral votes. If that happened, the election would go to the House of Representatives to decide. Setting aside the outcry that would result, it's worth considering what it would take for that to happen.
Now, let's enter the realm of speculation. If Johnson and Weld capture their home states (an "if" that should be in 89-point type, as we'll explain in a second), and if Trump manages to capture, say, Florida and Pennsylvania or Ohio, suddenly we end with no one having a majority -- and we're off to the House.
The last time a non-major-party candidate won a state was in 1968, when George Wallace captured most of the Deep South. It wasn't enough to keep Richard Nixon from getting a majority of the electoral votes, but it certainly didn't do Hubert Humphrey much good to gobble up states that, at that point, had almost always voted Democratic. (Though, notably, not in 1964.)
So could a Johnson-Weld ticket snag some states? Well...
Fox News released a poll on Wednesday suggesting that, in a three-way match-up with Trump and Clinton, Johnson would earn 10 percent of the vote. That's far better than he did in 2012, which is to be expected given the level of antipathy toward the two front-runners. But it's also almost certainly inflated by a general lack of familiarity with Johnson -- and an over-familiarity with his competition.
Weld wasn't part of that consideration, though. Weld served as the governor of Massachusetts for six years, resigning in 1997 when Bill Clinton nominated him to be ambassador to Mexico. (The Senate rejected his nomination.) He moved to New York, his home state, where he ran for governor in 2006, losing the nomination to John Faso (who himself lost the race in a landslide).
What Weld brings to the equation, then, is something of a base in the light-blue Northeast to match Johnson's something-of-a-base in the Southwest. He offers an opportunity to eat into Clinton's advantage to some degree in two northeastern states -- though probably not in any meaningful way in New York -- as Johnson could help eat into her lead in New Mexico. In theory.
In reality, it's probably not that simple. In the Fox News poll, Johnson pulled evenly from Democrats and Republicans -- about 8 percent of the vote among each -- while winning about a fifth of the independent vote.
A Johnson-Weld ticket, featuring candidates who last held statewide office more than a decade ago, would depend heavily on the ability to make people aware of their candidacies. In order to participate in the presidential debates this fall, the ticket needs to average at least 15 percent in five national polls close to the debate. That's a higher bar than it seems.
But Johnson may have an advantage that past third party candidates didn't: Financial support from the remnants of the Never-Trumpers. Johnson, who started out as one of the longest-shot Republican candidates in the 2012 cycle before switching to the Libertarians, isn't intertwined with moderate Republicans in the way that Weld is. Weld helped fundraise for Mitt Romney's presidential candidacy in 2008 and backed him in 2012. Earlier in this cycle, he endorsed John Kasich. If donors are looking for a Romney-type to challenge Trump and Clinton, how about another moderate former Massachusetts governor who's already going to be on the ballot?
Update: The Daily Caller reported that David Koch, of the "Koch brothers" Kochs, told Johnson that he could expect "tens of millions of dollars" in support for his bid. A Koch representative told NBC's Leigh Ann Caldwell that the report was incorrect.
What's presented above is the best-case argument for the efficacy of a Johnson-Weld ticket. It's highly unlikely that Johnson and Weld could split the vote enough in any state to actually prevail, making the give-it-to-the-House argument fairly useless. Wallace won states in 1968 by appealing to the Deep South's racism, a powerful motivator in the moment. Johnson and Weld (almost by definition) don't engender the same sort of passion.
What's more, in recent election cycles, partisans (and leaning independents) have been less inclined to stray from their party when voting for president. The prospect of handing the White House to Trump or Clinton in 2016 may further disincline Democrats or Republicans from toying around with Johnson and Weld.
The last, best chance to keep Trump or Clinton from getting to the White House may be the presidential candidacy of a guy who got 4,300 votes in the 2012 primary, about a third of the total earned by a guy named Fred Karger. Given the success of the stop-Trump effort so far, though, that's probably better than one might have expected.