During the 40 year battle with communism the United States underwent many changes of self understanding.
The first was a recognition, based on the term 'godless communism', that the United States was a religious nation. This led in 1953 to inserting the phrase 'under God' in the pledge of allegiance.
From that point on the country began to make many changes including full legal rights for Negroes, vast expansion of the immigration laws, and the radical understanding that America was a free market economy. The latter elevated the entire argument in favor of commerce and against government control. A battle that the free market has been slowly winning since the mid-1960s.
It seems that our enemy helps us define ourselves.
So how will our enemy, Islamism, help us define ourselves today?
Islam clearly has an inferior status for women. That was already changing in the U.S. and will be even more aggressively changed in the coming years. Islam is only divided into two sects, and as a consequence neither sect has much internal argument about important issues such as science, economics, philosophy, or political life. The ideas of freedom are nonexistent in Islam.
I would suggest that all of these issue areas will come under scrutiny and result in change in the United States over the next few decades.
The first change I noticed is the increased willingness of Americans to debate many issues and an increasing willingness of individuals to carry on debates with their friends and peers. I think this is a reaction to the mono ideology of Islam.