The impact of independent and third party candidates in American elections is usually small, and even where it is measurable, it is often overestimated.
Take the 1992 and 2000 election as examples. Democrats are convinced the Ralph Nader cost them Florida. The problem with this analysis is that everyone in Florida knew perfectly well that Nader could not win, and that either Gore or Bush would become President. Those that voted Nader did so because they could not abide either Gore or Bush, and if Nader had not run, they would not have voted. Also, as Nader himself has pointed out, more registered Florida Democrats voted Bush than voted Nader. Al Gore lost Florida all on his own.
In 1992, some Republicans claim, Perot cost Bush the presidency. There is a little more credibility to this, as Perot got 20% of the vote, not 2%. But, again, many from were people who would not otherwise have voted. The turnout rose from 50% to almost 60%. Perot got 19 million votes, yet Bush's vote was down by just 10 million from 1988. Clinton's vote was up by three million compared with Dukakis's performance. So, the Republicans were down by 10 million and other parties up by 22 million. Did Perot take 10 million votes that would otherwise have gone to Bush? Possibly, but I doubt it. Breaking his "no new taxes" pledge would have cost Bush votes with or without Perot. If Perot had not run, Bush would have got more votes than he did, but still underperformed his 1988 total, and Clinton's vote would also have been higher. The election might have been closer, but I doubt that Bush would have won.
So, might an independent or third party run affect the result of the next presidential election? Well, it is always possible. But a score of 2% as minor parties usually manage is not likely to do it. Even a bigger vote won't if, like Perot's, it is fairly evenly spread across the country.
But if it is concentrated in a few states, that might be a different story.
(More on this at a later date)