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.
Factions in the Republican Party (United States)
In economic policy, conservatives call for a large reduction in government spending, free trade, less regulation of the economy and personalized accounts for Social Security. Supporters of supply-side economics predominate, but there are deficit hawks within the faction as well. Before 1930, the Northeastern pro-manufacturing faction of the GOP was strongly committed to high tariffs, but since 1945 it has been more supportive of free-market principles and treaties for open trade. The conservative wing supports social conservatism (often termed family values) and pro-life positions.