Conservatism and liberalism have influenced American society by providing different perspectives on the proper course for social and economic issues. Currently, there is the tendency to suppose that liberals support big government and social reform while conservatives support limited government and social traditions. While those definitions do reflect the fundamental (or perhaps fundamentalist) core beliefs and ideologies of conservatism and liberalism, this limited way of positioning two belief systems as inherently oppositional has led to problems.
Many citizens, as well as politicians, have become brainwashed by this opposition. While there are exceptions, people who don't mindlessly agree with the positions of their party, it has gotten to the point that if one happens to be a conservative, he/she feels inclined to disagree with a liberal simply on the misguided belief that he/she must disagree with liberalism in general. The reverse is also true. The current political climate, for citizens and politicians, has unfortunately become guided, not be productive conversations, but by mindless gainsaying (disagreements). It has become quite ridiculous.
Conservatism and liberalism (and past productive syntheses of these viewpoints) has benefited American society, but currently there are too many people who favor one viewpoint so strongly that they have basically given up on being open to different ideas, and many politicians have given up on compromise. This has become a serious problem for the general intellectual growth of America and it is also a problem for American society because some politicians are too stubborn to compromise and therefore, nothing in Washington gets done.
It is a little bit hard to say whether liberal and conservative thought have influenced American society or whether liberal and conservative thought grow out of American society naturally. One way or the other, we can clearly see strands of liberal and conservative thought in American society.
We can see conservative thought most clearly in the attitudes of many Americans towards religion and religious teachings. Conservatism tends to favor religion since religion has traditionally been a major influence on society. We can see this in American society in the need for major political figures to profess a deep faith in God. We can see it in the tendency of many people to base attitudes towards such things as gay marriage on their religious beliefs.
However, liberalism has a major impact on American society as well. At least since the New Deal, liberal economic thought has dominated American society. People tend to believe that the government should be responsible for the economic health of the society. Only the very most conservative people believe that the government should stay out of areas like providing Social Security and Medicare.
American society shows attitudes that come from both liberal and conservative thought.