I would use neo-liberal to describe many American politicians, including a majority of Democrats, as they tend to have views right of center. But I would use liberal to describe many of the people voting Democrat as their views reflect positions that are at least center left.
In the US we use liberal to refer to people left of the American center which is already skewed right. Liberals are center right.
I would say that American politicians are skewed to the right, but the American people themselves are not.
Progressive ideas are popular with Americans.
I would use neo-liberal to describe many American politicians, including a majority of Democrats, as they tend to have views right of center. But I would use liberal to describe many of the people voting Democrat as their views reflect positions that are at least center left.