The idea that American needs to be great again seems to me to come at least partly from the idea of American Exceptionalism. I capitalize Exceptionalism because it is usually presented as a philosophy or even as a matter of faith (as opposed to being merely a sort of historical observation). People on this blog have used it as a personal belief, even though Donald Trump doesn't believe in it and one pope actually wrote an encyclical against it.
The concept turns out to be complicated, because its meaning has changed over time. According to Wikipedia, there are three aspects to it.
1. There is something called "Americanism" based on
...liberty, egalitarianism, individualism, republicanism, democracy and laissez-faire for business.
2. The United States has a mission to transform the rest of the world according to the tenets of Americanism.
3. Because of the tenets of Americanism and because of its mission, America is superior to other countries.
An interesting thing about the American experience at the founding was that America was not founded on the basis of any particular culture. It was founded on the basis of rational principles of citizenship and a rational moral order. It is true that the founders themselves were mostly Protestants and all were white. But when they broke from England, they did not extablish the country as a little England for (former) Englishmen. It was established as an order for all (the "all" being more narrowly defined than now).
Humans being human have tried to tribalize this order over time and they still are today. The order originally excluded blacks and women from full participation. It excluded Asians and Africans and Indians. Over time, the veil of equality has spread. Each time it has moved, people already under it, people who in the past would themselves have been excluded, have argued that they new people don't deserve the rights of the old. Arguments have been made that the republic was specifically a white Protestant Christian republic, then a Christian republic, then a Judeo-Christian republic. As America has gone abroad to civilize other countries in Asia, Africa and the Middle East, there is still talk about American values as being Judeo-Christian values as we try to convince non-Christian countries that our values are universal.
American exceptionalism is a good thing, if we look at how remarkable it is compared to what other options were available at the time of our founding. It's a very bad thing when we believe that our "exceptionalism" makes us better, or somehow not bound by international laws. The democracy has grown and prospered and enlightened other peoples only when it was stripped of its tribalism. The American republic only works as a secular republic. A secular republic will be considered an anathema to other countries who thing that they are exceptions, as will a Judeo-Christian republic be anathema to non-Christians. But the secularism of our republic, which is the thing that made us so exceptional, was specifically designed to be able to contain religions. It has only worked where it was able to contain other religions in other places.
If American exceptionalism is a sort of religion, then American nationalism is its heresy.