You asked the question.
" In what way are liberals here in America adopting the same popular debauchery and immorality that lead these once powerful advanced societies into the dust that will keep us from meeting their same fate ?"
Liberals do not exist in the United States as of now. What we are dealing with are Progressives. That group espouses a totalitarian ideology of controlling nearly every aspect of a person's life because they do not adhere to the principle of inalienable human rights. The rights of life through the keeping and bearing of arms, liberty through the freedom of speech, religion, and assembly, and property/happiness through being secure in one's persons, papers, and effects stand in the way of the Progressive agenda. This has been illustrated in nearly all of the policies put forward by the Progressives in both major Parties of the US. Liberalism embraces freedom, but that freedom relies on a moral and just citizenry.
As John Adams put it:
"It is religion and morality alone which can establish the principles upon which freedom can securely stand. The only foundation of a free constitution is pure virtue."--(Source: John Adams, The Works of John Adams, Second President of the United States, Charles Francis Adams, editor (Boston: Little, Brown, 1854), Vol. IX, p. 401, to Zabdiel Adams on June 21, 1776.)
Debauchery and licentiousness beget totalitarianism. The idea of "I'm special and thus should rule over you/others" comes from the degradation of morality in society. For example, treating homosexuality as anything other than a mental disorder was a political move in the 1970s, not a scientific one. The diseases rampant within the gay community alone is proof of how dangerous this lifestyle is. How does that effect policy in other areas? It sets a precedent that individuals with mental disorders are not in fact sick, but just different. Next will be the move to "normalize" pedophilia. The DSM V already attempted to do this, but outrage at the reclassification of pedophilia as a "life style choice" was rejected: for now.
How does this correlate to the fabric of a society and how does it contribute to its fall? The quality of character of the individuals within the society will determine the quality of its leaders and thus the more licentious a society becomes the more their leadership will engage in and impose debauchery. Immorality is lethal to any Republic that uses a democratic system because the voters in that system will not make good choices for leadership. Idiotic reasoning and irrationality take hold based not on fact but rather the fantasies of any group pushing an agenda. The global warming debacle being a good example of this Peter Pannery.
The Roman Empire is a great example of this as the immorality of the aristocracy of that society moved it from a civilization working for its people to an Imperial system that served only the rich and powerful to the point that the legions could no longer defend the borders (due to lack of funds) and the Empire itself fractured over power struggles between would-be dictators. Our own society is going through a polarization due to the Progressives attempt at "fundamentally transforming" the US into a more soviet style system. Again, both parties are responsible for this through the militarization of our domestic police forces, and the subsequent disarmament of the civilian population.
John Adams explained the danger of allowing a society to degenerate into immorality because they (the Founding Fathers) did not wish to legislate morality. They expected the citizenry to self-regulate and adhere to the philosophy found in the Bible. Since we have not, and we have allowed ourselves to degenerate into a society of whore-mongers, sluts, and sodomites we deserve the collapse that has already begun.
"[W]e have no government armed with power capable of contending with human passions unbridled by morality and religion. . . . Our constitution was made only for a moral and religious people. It is wholly inadequate to the government of any other."--(Source: John Adams, The Works of John Adams, Second President of the United States, Charles Francis Adams, editor (Boston: Little, Brown, and Co. 1854), Vol. IX, p. 229, October 11, 1798.)
Thomas Jefferson made clear the importance of morality in the Republic they were creating.
"Give up money, give up fame, give up science, give the earth itself and all it contains rather than do an immoral act. And never suppose that in any possible situation, or under any circumstances, it is best for you to do a dishonorable thing, however slightly so it may appear to you. Whenever you are to do a thing, though it can never be known but to yourself, ask yourself how you would act were all the world looking at you, and act accordingly. Encourage all your virtuous dispositions, and exercise them whenever an opportunity arises, being assured that they will gain strength by exercise, as a limb of the body does, and that exercise will make them habitual. From the practice of the purest virtue, you may be assured you will derive the most sublime comforts in every moment of life, and in the moment of death."--(Source: Thomas Jefferson, The Writings of Thomas Jefferson, Albert Bergh, editor (Washington, DC: Thomas Jefferson Memorial Assoc., 1903), Vol. 5, pp. 82-83, in a letter to his nephew Peter Carr on August 19, 1785.)
So, in answer to your question, the Progressives are acting in every way that caused the fall of Rome's character, and lead to the poor leadership that allowed the barbarians from the north and in fighting from within (due to greed) to unravel the once great and powerful Roman Empire. Morality plays a very large role in the types of people that lead these societies. If the society cannot produce a quality leader, like a George Washington or Caesar Augustus because the people themselves are immoral, then we get a Nero or an Obama.
I hope that adequately answers your inquiry.