I don’t consider myself a centrist, I am certainly a liberal on most things political. I may not agree with the effectiveness of a third party of the center, but in today’s extremely polarizing political environment, a movement for such a party would wake the two parties towards being more reasonable about opposing viewpoints.
A centrist third party, or more realistically a political movement from the center could very well have the effect that the progressive movement of the late 19th, early 20th century had with the two parties, in that case especially the Democratic Party. In this case a centrist movement would make both parties look long and hard at itself and perhaps begin taking a more moderate approach to dealing with opposing views.
The problem of the two parties goes beyond the idea of both parties moving to ideological extremes, but rather neither party seems willing to look each other in the eye and work on the issues at the center of people’s lives. While fighting tooth and nail over more ideologically driven issues, they forget most people want a good job, access to health care, a retirement they can depend on, and home they can call their own. In other words, the people care about what I would call “brown bag” issues that more directly affect our day to day living. A lot of our elected officials have forgotten about that, and seem more concerned with just beating the other side of the political aisle.