Tim, you seem to know what & when I'm doing it. Don't tell to much. 
And, for the sake of discussion, if Christians fled England to escape the Church of England
(the state imposed religion), to find their 'own' country to be free to follow their Christian faith
(not a state imposed denomination), wouldn't that new country (at that time) be considered a
'Christian Nation?'
For instance, just as Saudi Arabia would be considered a 'Muslim Country,' even though there are some who don't practice the traditional Sunni approach to Islam, or the few thousand practicing Christians, Jews, Hindu, Buddhists, etc.
By a lot of the founders writings it appeared they considered this a Christian Country. (More on that, later.)
In the sense that today we put labels on things our modern concept would clearly identify nations by their primary religious affiliation. However the bible never does this. I could only find the phrase Jewish nation in one place in only the NIV. I checked Strongs concordance and the reference is to a race of people not a religion.
(John 11:51-52 NIV) He did not say this on his own, but as high priest that year he prophesied that Jesus would die for the Jewish nation, {52} and not only for that nation but also for the scattered children of God, to bring them together and make them one.
(John 11:51-52 NASB) Now this he did not say on his own initiative; but being high priest that year, he prophesied that Jesus was going to die for the nation, {52} and not for the nation only, but that He might also gather together into one the children of God who are scattered abroad.
(John 11:51-52 KJV) And this spake he not of himself: but being high priest that year, he prophesied that Jesus should die for that nation; {52} And not for that nation only, but that also he should gather together in one the children of God that were scattered abroad.
51 And <G1161> this <G5124> spake he <G2036> not <G3756> of <G575> himself <G1438>: but <G235> being <G5607> high priest <G749> that <G1565> year <G1763>, he prophesied <G4395> that <G3754> Jesus <G2424> should <G3195> die <G599> for that <G5228> nation <G1484>;
52 And <G2532> not <G3756> for that <G5228> nation <G1484> only <G3440>, but <G235> that <G2443> also <G2532> he should gather together <G4863> in <G1519> one <G1520> the children <G5043> of God <G2316> that were scattered abroad <G1287>.
53 Then <G3767> from <G575> that <G1565> day <G2250> forth they took counsel together <G4823> for to <G2443> put <G615> <G0> him <G846> to death <G615>.
John 11:51-53 (KJV)
Strongs Concordance
1484. ethnos, eth'-nos; prob. from G1486; a race (as of the same habit), i.e. a tribe; spec. a foreign (non-Jewish) one (usually by impl. pagan):--Gentile, heathen, nation, people.
The real problem I have with attaching religious descriptors to nations is that in most cases these nations aren't theocracies. We deal with them according to their political ideology and their laws. Some nations have enacted sharia law (
http://en.wikipedia.org/wiki/Sharia ) and in those cases where their religion defines their political ideology and their law they must be dealt with according to those descriptors.
If 95% of the people in the US were Christians even if 99% of them were Christian we still couldn't refer to ourselves as a Christian nation. It wouldn't be accurate. I personally wouldn't be comfortable living in a nation that formed their laws with the idea of a religous ideology.
Let's say I was a Charismatic/Pentecostal and the laws were based on Southern Baptist theology. A goodly chunk of what I believe would be outlawed. Ok, so if we form the laws in such a way that we embrace the lowest common denominator among those denominations that are considered Christian where do we stop? You see the problem?