As far as I know, there is no Scripture that specifically supports an "ultra-patriotic" perspective.
There are, however, a number of places in the NT where followers of Christ are instructed to obey the laws of their respective nations, insofar as those laws do not contradict God's commands. The primary intention was (is) to ensure that Christians would not bring themselves into disrepute, which would cast Christ in a negative light and would encourage the many people who sought to do harm to the church -- two things that Christians would certainly want to avoid doing.
A few references:
And Jesus said to them, "Whose likeness and inscription is this?" They said, "Caesar's." Then he said to them, "Therefore render to Caesar the things that are Caesar's, and to God the things that are God's."
Remind them to be submissive to rulers and authorities, to be obedient, to be ready for every good work, to speak evil of no one, to avoid quarreling, to be gentle, and to show perfect courtesy toward all people.
And especially 1Pe 2:12-19:
Keep your conduct among the Gentiles honorable, so that when they speak against you as evildoers, they may see your good deeds and glorify God on the day of visitation. Be subject for the Lord's sake to every human institution, whether it be to the emperor as supreme, or to governors as sent by him to punish those who do evil and to praise those who do good. For this is the will of God, that by doing good you should put to silence the ignorance of foolish people. Live as people who are free, not using your freedom as a cover-up for evil, but living as servants of God. Honor everyone. Love the brotherhood. Fear God. Honor the emperor. Servants, be subject to your masters with all respect, not only to the good and gentle but also to the unjust. For this is a gracious thing, when, mindful of God, one endures sorrows while suffering unjustly.
Edit to address more parts of the question:
As far as I know, the correlation between "ultra-patriotism" and "cultural Christianity" is primarily an American phenomenon, though I'm not particularly familiar with the state of the church in other countries. And there is certainly disagreement on the subject even within the US.
For example, several years ago, when current US President Barack Obama was making an international tour at the beginning of his first term in office, he stated the United States "[was] not a Christian nation." The "ultra-patriotic" Americans to which your question refers can often be heard lamenting that statement, even today.
Also relevant is the traditional understanding of the US as a nation that was founded by English emigrants who were dissatisfied with the authority exercised by the Church of England -- though I'll leave it to someone who knows more about that part of history than I to expound on the details. It all ties together with the American emphasis on freedom and the resultant emphasis on individuality.