It's been fashionable for some time, but even more after 9/11 (sorry, have to reference it) to compare the United States to Rome. We did get rid of slavery, of course, but there are many parallels.
A republic that continually became more and more oligarchic? Check. We've not become dictatorial yet, but ... who knows who might exploit the War on Terror how far?
An empire, even if we have no emperor, and one that uses a mix of hard and soft power, force and money, alliances and more? Check.
A polyglot nation, with many ethnic and social groups? Check.
But, there's nations besides Rome that have lessons from ancient history.
Egypt? Divisions at semi-regular times between Upper and Lower Egypt reflect red-blue divisions today. Ultimately, both sides lost. (That said, when the divisions are ideological, on one side, the other side can't be so pragmatic as to play Preznit Kumbaya, either.)
Also, let's not forget that ancient Egypt, like today, had climatic variations. Global warming aside, anti-science attitudes in the U.S. could learn lessons. Egyptian pharoahs monitored Nile levels every year, so as to predict how good or bad the annual fertilizing flood would be.
At the same time, pharoahs eventually extended the trappings and sharing of power beyond blood lineage, co-opting exceptional commoners.
Finally, beyond authoritarian government, pharoahs co-opted religion in a way Roman emperors never did. That's a definite lesson for today.
China? Similar lessons to Egypt in some ways.
Throw out the Tibet and Xinjiang which ethnic Han dynasties didn't always control. China proper was often split into competing northern and southern empires at the same time. In the north, especially, weather issues with the Huang Ho (Yellow) River were important. Chinese emperors didn't co-opt religion in the same way as in Egypt, but did claim the "mandate of heaven." And, Chinese developed their mandarians, complete with Confucian schools and exams for civil service.
In America today, if it stumbles further, it's not because America is no longer a "Christian nation." It's because the belief that we were in the first place has both ossified and become malignant at the same time. It's because (as what partially happened in Egypt) geographic distinctions get appropriated for religious or other ends. It's when the elite let themselves be co-opted to the national security state, even if it doesn't have an emperor or pharoah at the top.
With both ancient nations, they should advise anybody not a Christian fundamentalist that claims we are a "christian nation" not only are ossified, they mean nothing when enlightened by the stark realities of history.
Finally, given larger forces of history, Rome and China, at least, maybe needed to fall, from sheer size, both geographically and in terms of population. Let's not forget we have more than 310 million in America now.