Can the US be one nation without being 'one nation under God' and why?

Of course it can- it already is. The United States is a secular nation with a secular government in spite of all the little mentions of gods the religious have managed to thrust into our nations fabric. Believing in a god does not cause it to exist, just as believing the Earth is flat never made it any less spherical.

Answer

Look at history and you will see how nations who have eliminated God have fallen. Rome is the classic example of an "unbeatable" empire that fell to its knees. True unity, real peace, can only be experienced through God. If we submit to Him, then we submit to His Word as the standard by which we make all laws, conduct business, make economic decisions, etc. If we all have God as our unifying source, we could truly be one. Without God, there will never be unity not in our nation or any other.
  • Yes. It has absolutely nothing to do with religion or secularism and everything to do with the educating all citizens to respect the rights of others and the government to abide by the Constitution as was intended.

Answer

Looks like people didn't do their homework. America was founded and the Puritans came into order. Although their religious beliefs were crude (burning witches at the stake, etc.) it was a way of rule amongst people that could become chaotic.

Answer

The phrase ¨One nation under God¨ was added to the US Pledge of Allegiance on Flag Day on June 14, 1954. To suggest that ¨The US cannot be one nation without being ¨under God¨ would deny the validity of the nation´s previous 178 year long existence.