The New Deal completely changed Americans' attitudes towards the role of government. Before the New Deal, many or most Americans believed that the government had no real role in maintaining the health of the economy or in providing for people who were too old to work or who were otherwise unemployed. The government was supposed to set tax rates and tariffs and things like that, but it was not supposed to otherwise intervene in the economy.
After the New Deal, this all changed. Americans came to accept the idea that the government would be responsible for the performance of the economy as well as for the well-being of the people. We have come to accept this to the extent that even budget cutters in Congress say they will not touch Social Security or Medicare. These are programs that were unthinkable before the New Deal but which are seen as indispensable by many Americans today.