Varieties of criticism
Conservative criticism has nothing much to do with "left-wing" or "right-wing", because left-wing people are often very conservative, in the defined sense, while right-wing people can also be very radical, in the defined sense. The difference between "radical" and "conservative" has more to do with the belief in whether "a change to something genuinely new" is really possible and necessary. Radicals typically believe strongly that such change is highly desirable and necessary, and that it can be achieved. Their criticism is that there is "not enough" change. Conservative critics, by contrast, are very skeptical about any such change, because they feel the change is really "just another form" of something that already exists.
List of American conservatives
American conservatism is a broad system of political beliefs in the United States that is characterized by respect for American traditions, republicanism, support for Judeo-Christian values, moral absolutism, free markets and free trade, anti-communism, individualism, advocacy of American exceptionalism, and a defense of Western culture from the perceived threats posed by socialism, authoritarianism, and moral relativism. The recent movement is based in the Republican Party, though some Democrats were also important figures early in the movement's history.