The issue is two-fold: Scarcity and the sword.
Let's start with scarcity. As I describe in my book the Slavery of Death, human life is governed by a survival ethic in a world of perceived and actual scarcity. This plays out both personally and institutionally. We have to survive. And to survive we have to secure resources and defend against threat.
At the level of the nation state, the realities of scarcity demand that the state act in ways to secure and protect its survival. Thus, nations must place their political and economic interests above the interests of other nations and peoples. Nations create, secure and regulate borders. Nations engage in monitoring, policing and eliminating "threats at home and abroad." Nations do so through ethically dubious activities like mass surveillance; black ops; torture; enhanced interrogation; spy craft; sabotage; dealings with evil agents, power brokers and rouge nations; drone strikes; and other sorts of lethal force, both inside and outside its borders. Lastly, nations make war.
The list can be expanded upon, but everything on such a list is driven by a nation's survival instinct. And within history I don't see how any nation can escape this destiny. True, there is a continuum of darkness here, but any entity that places its own survival over the survival of others cannot ever be described as "Christian." At the heart of Christianity is the kenotic, cruciform life of Jesus. And no nation state within history can emulate this example. This is not to deny that nation states can do many good things to provide space and structure for human flourishing, but those spaces and structures are ultimately dependent upon the ultimate telos of any nation state: survival at any cost. Place that survival at risk and spaces and structures of flourishing will rapidly shrink or evaporate. And if they don't, another nation will invade and wipe them out. Nations can't be pacifists. Every space and structure within a nation that we might be tempted to label "Christian"--because that space and structure is just and fair--is wholly dependent upon patrolled borders, policing, mass surveillance, standing armies, vast spy networks, weapons of mass destruction, and on and on and on. Don't miss the forest for the trees. No nation state can operate in a "Christianly" way.
Relatedly, the sword. What is a nation or state exactly? Many political theorists boil it down to this: a monopoly on lethal violence. Citizens can't kill each other. But the police, acting on behalf of the state, can shoot you. The state can also execute you. And well before guns or electric chairs show up, there are all the coercive uses of power, from legal fines to locking you up in a jail or prison. All of it backed up by the state's monopoly on violence.
This casts a long and dark shadow over any aspirations to create or establish a "Christian nation." Sure, you might pass bills or get Supreme Court decisions in your favor which align with a particular Christian "value." But what we're not talking about his how that value is being backed up by coercive power and lethal violence. Simply stated, we're "winning back the nation for Christ" at the point of a gun. But threatening people with police force isn't how Jesus goes about his business.
That is what is often missed by Christians wanting to restore "Christian values" to America. Sure, on any given issue we might be able to discern a position that is more or less "Christian," and work to get that value enshrined in law. I'll grant you that. The notion is that, if this culture war battle is won, the nation becomes more "Christian." Trouble is, that value, if enshrined, is now being backed up and enforced with coercive power. And that's a problem. Politics is a fight to see who gets to control the monopoly on violence. If you win your culture war battle, you're effectively pointing a gun at every non-Christian in the nation and forcing them to comply. So while the value you're wanting to protect or defend might be admirable, and even "Christian," the enforcement of that value by a state calls the whole thing into question.
The other option here is classic liberalism, which many Christians endorse (David French is an example). In this view, the state uses it coercive power to create a "public space" where diverse views and life choices can be expressed. Thus, a Christian might defend the right to gay marriage. Not because they agreed with it, but because they don't think the lethal violence of the state should be used to police what people do in their bedrooms. People have the right to live their lives as they see best, even if that goes against God. In this view, the state's job isn't to adjudicate between Christian and non-Christian values, but to create a public space for people to live their own lives however they'd like. Trouble is, if this is how the state uses its power, the resultant public space won't be "Christian."
So you're damned if you do, and damned if you don't. If the state creates a neutral public sphere, the nation won't be "Christian." But if the state chooses to enforce Christian values at the point of a gun, that's not "Christian" either. Either way, there is no "Christian nation" on the political horizon.
To sum up, again, I'm not saying states can't be better or worse. Nor am I saying Christians shouldn't involve themselves in democratic politics to make states better. What I'm trying to describe is how the label "Christian" is simply impossible for any nation state. States are governed by the imperatives of self-preservation. And states enforce their way of life at the point of the gun. Those things preclude any application of the adjective "Christian" to any nation state.