The problem's not so much whatever group of religious differences between Judaism, Christianity, Islam and any other religion. It isn't whose god or interpretation of God is the "true" God.
Belief in the Godhead or its lack of is bigger issue. Nowadays we can't say "God bless America" without some idiot complaining about the word "God."
To make matters worse, non-believers do have their own gods -- money, greed (any or all of the seven deadly sins to be included in this list), Darwin (evolution) and themselves. This is such hypocrisy that punishes believers in order to make this little population of the nation happy.
Other cultures (even those within the US) make constant references to God (Jehovah, Allah, Buddha, Krishna, Ra, etc) in their day-to-day speech. This is something rarely found nowadays in US English heavily tainted with political correctness. At least, it's good to know that this isn't true in other cultures.
The Muslim greeting "Salem malenku" is both a greeting and a blessing. The expression means "May the peace of God be with you."
The Arabic expression "Insh'allah" means "God willing" and it expresses the hope that God would allow something to happen. This expression was adopted in Spain as "Ojala."
At the same time, the Spanish goodbye expression "Adios" means "Go with God," which comes from the Latin expression "A Deus." The same remains true for similar expressions like "Adiu" in French. Unfortunately many of the people using this and similar expressions aren't aware of the religious meaning of these words and phrases.
In Hebrew, a person may say "Shalom" as greeting which means "May God be with you." Although Hebrew doesn't have as many references to God in its speech, worldwide most people consider Hebrew as the language of the People of God.
In English (American especially), the expressions "For God's sake" and "(May) God bless you" have rather been changed to accommodate atheists and others. These expressions have changed to "For Pete's sake" (even "For fuck's sake") and a generic "Bless you" or the German expression "Gesundheit," which means "healthiness." Expressions like "In the year of our Lord" are no longer common, but at least it survives in classic English literature and poetry.
At the least, the common expression "(May) Lord help us" or "(May) God help us" is still used as a reminder that this is a nation of believers (82.31% of Christians, 1.77% of Jews, 1.58 % of Muslims; 2006, http://www.thearda.com/internationalData/countries/country_234_1.asp) by many including Presidents.
