It seems to me that what Pope Leo is saying is this: if the government goes against the will and laws of God then their authority is no longer valid, in fact, its null and void. I can think of many governments who go against the will and law of God, including the US government.
I shall refer you to CCC 2242, which you, as a Catholic are bound to obey
"The citizen is obliged in conscience not to follow the directives of civil authorities when they are contrary to the demands of the moral order, to the fundamental rights of persons or the teachings of the Gospel. Refusing obedience to civil authorities, when their demands are contrary to those of an upright conscience, finds its justification in the distinction between serving God and serving the political community. "Render therefore to Caesar the things that are Caesar’s, and to God the things that are God’s."48 “We must obey God rather than men.
When citizens are under the oppression of a public authority which oversteps its competence, they should still not refuse to give or to do what is objectively demanded of them by the common good; but it is legitimate for them to defend their own rights and those of their fellow citizens against the abuse of this authority within the limits of the natural law and the Law of the Gospel.”
So if a government passes laws that go against natural law and the Law of the Gospel, then you are bound not to follow those laws, but to follow other laws that do not go against natural law and the Law of the Gospel. Even if a government oppresses you, you are still bound to follow their laws (so long as those particular laws do not go against natural law and the Law of the Gospel). Therefore even an oppressive regime has, while it is still in existence, authority.
So yes, the US government certainly does have authority (and it hardly classifies as an oppressive regime by any stretch of the imagination). You are bound, by Church teaching as a US citizen, to follow the laws of your country (just as I am bound to follow British laws). Apart from, of course, laws that go against natural law and the Law of the Gospel.
I really fail to see why you have such an issue with this. It is the teaching of our Church.
These are not my personal views, they are the teachings of the Church. Ant-authoritarianism runs contrary to Church teachings.