Yes.
"If a society is not bound together by collectively accepted moral values -- as America was during its Judeo-Christian era -- then what holds the society together?"
Society is still held together by collectively accepted moral values. It is still wrong to cheat, steal, rape, murder, etc. Whenever you find someone being taken advantage of by force or fraud, society almost to a man collectively disapproves.
"What do the members of the society have in common?"
Plenty. Our adherence to the Constitution of the United States, and a love of freedom.