I actually wrote my undergraduate honors thesis on the role of third party and independent presidential candidates in modern U.S. elections, so this is an area of great interest to me.
The short answer is, no, it is not possible for a viable centrist party to emerge in the United States. The two-party system is hardwired into our constitution and our electoral system.
Duverger's law states that the combination of single-member districts and simple plurality elections will tend to produce a two-party system. While Maurice Duverger never intended for this to be an absolute limitation, the theory describes the situation in the United States very well.
Duverger's law basically functions through two principles:
1). The Mechanical Effect- The mathematics of an SMSP electoral system leave little incentive for smaller parties to form and run candidates. A party that consistently win the support of 15% of voters nationwide might still not win a single seat in the legislature. There is no consolation prize for coming in 2nd or 3rd place in an individual congressional district. (It it important to note that Duverger's law is better understood as a prediction of the number of parties that will be represented in the legislature, not necessarily the number of candidates that will appear on the ballot).
2). The Psychological Effect- If 3rd parties do run, voters won't vote for them even if they are a voter's first preference because a rational voter doesn't want to waste their vote, or worse, produce a spoiler effect that sees their least-preferred candidate win (the Nader problem).
In the United States, these effects are somewhat compounded by our Presidential system. Even a party that might be able to win a handful of seats in the House would be delegitimized in the eyes of the electorate because they would never be able to compete for the big prize- the White House.
This all being said, a at least temporary third party in the "radical center" could work but I don't know how. In 1992, we had a real 3-way horse race, right?
While 1992 and the tale of Perot and then the Reform Party is often cited as evidence that there can be some "give" in the two-party system under the right circumstances, the example also sort of demonstrates why we can't have a third party here.
First, we didn't actually have a 3-way horse race. Ross Perot's 19% of the vote got him a grand total of zero electoral votes. Perfect demonstration of the effect of SMSP rules. Now, it is true that at his peak in June of 92 Perot was considered the frontrunner, polling ahead of both Bush and Clinton with ~37% of the vote. But his numbers were trending steadily downward by the time he fake-dropped-out in July. Part of that was because he ran an increasingly incompetent campaign, but a great deal of it was inevitable once Democrats rallied around Clinton. A big part of Perot's campaign relied on displacing the democratic nominee as the principle opposition candidate to Bush.
But I digress. The real problem for third parties is demonstrated by what happened to Perot's movement in the immediate aftermath of 1992. When a credible third party challenge does emerge, one or both major parties will move to neutralize the threat by co-opting the third party's platform. Perot's campaign focused on the budget deficit, a major issue that was being largely ignored by both major parties. He also pushed various reform proposals that resonated well with voters but that the major parties had shown no interest in. Perot pulled supporters from both parties and turned out many other voters who might normally stay home, but Republicans were left feeling the most threatened by the Perot movement and blamed Perot for Bush's loss in 1992. So the party moved quickly to capture the Perot coalition. The Republicans essentially copied-and-pasted Perot's platform into the Contract With America, ran on that in 1994, and swept into both houses of congress. Balanced Budget Amendment, term limits, de-emphasizing social issues. Republicans were purposefully using campaign rhetoric directly modeled on Perot's messaging from two years ago. Once the Republican Party embraced the heart of Perot's platform, the wind was taken out of the movement's sails. By the time Perot actually formed the Reform Party, there was little need for it because the heart of it had already been absorbed into Republican Party. Perot himself only got 8% of the vote in 1996, and the Reform Party candidates for congress throughout the country didn't do any better.
The lesson is that when any third party movement does reach the kind of critical mass that would make it a legitimate threat to major party dominance, the best result it can hope for is to get the major parties to respond to it.
So sure, you could argue that the two parties have gotten so polarized right now that a significant portion of the American public would support a centrist party. You could even have an election where a strong third party or independent presidential candidate could emerge. But their relevance would never last more than one cycle. They'd make their point, probably still lose, and then the two parties would be forced to move towards the center.
By the way, it's important to distinguish a single independent candidate from an actual third
party. We do get a random independent senator or governor here and there, but it never really makes a meaningful dent in the two-party dynamics of American politics. Let's assume Perot could have run a better campaign and actually won the 1992 election. Or maybe Bloomberg or whoever could do it today. Then what? They'd have no natural base of support in congress. Worst-case scenario: horrible gridlock and a generally ineffective administration likely limited to one term. Best-case scenario: They'd make some compromises to get some centrist bipartisan measures through congress, but there'd be no infrastructure in place to affect any lasting change after that president left office.
TL;DR: Not gonna happen.
