Divine destiny is not a divine covenant. The only nation on this earth that has a covenant with God is Israel. The US is not the new Israel. Israel is and ever shall be Israel.
The Ten Commandments served as the preamble to the suzerain covenant that was both God's moral law and their national constitution. Let's not forget that. It is our moral code, not our national constitution.
The Christian church was at its best when it was under persecution. We've grown too comfortable in our churches and pews. Our churches, and, yes, by that I mean OUR churches, not just the truly liberal and neo-orthodox churches, have grown complacent and doctrinal anemic. We are like Ephesus...sound theologically, mostly sound ethically, but we've grown complacent and left our first love. A Christian nation will not make people more spiritual or more Christian. God does that on His own. God will bless the nations in which His people are present and who are serving Him themselves. His hand restrains evil for the sake of the presence of His people. His people, not the people of those nations, are those called to repent and return to their God.
Are there historical records of nations where Christian societies have thrived? Certainly. The First and Second Great Awakenings both had long lasting effects. Abraham Kuyper in Holland established a political and social movement based on Reformed doctrine that thrived in Holland for many years. In all those cases, the results were a natural result of the working of God in the hearts of men, established upon evangelism and sound doctrinal teaching. The effect on society was an UNINTENDED side effect that only became intentional when people realized what was going on. The bottom line is that we are called to be salt and light in a lost society. Withdrawing from that society abdicates those mandates, and acting as if we are a Christian nation changes souls is to ignore the radical depravity of man.
Christians are now and shall be until the Lord returns for His church the minority in any population. Jesus said that in the last days, it would be very like the days of Noah. I can not help but remember that Noah and his family were the only godly people on earth in those days. So shall it be for us.