You may think you have had a center left democratic party and center right democratic party in the past, but that's not how other western nations perceive you - many would say that the democratic party is center right, and the republican party is far right. Even before Trump.
Center is defined by where the wings are, and that in turn depends on how much you're looking at. Among developed countries, US is definitely on the right. But in US politics, Democrats are on the left.
