As far as government IDs, I would be hard pressed to think of a major country which does not have some way of identifying a citizen from a non-citizen. We already have these forms in place, such as passports, social security cards etc. State records, such as birth certificates and marriage licenses, are given credence in other states under federal law. A passport by definition identifies citizenship in a country. So all the federal gov't has to do is mandate all citizens are required to get passports and the problem of an additional national identity card is moot.
As far as making English the official language of the US, that is a far stickier point. I personally am of the opinion that when a person lives in a country s/he should be expected to learn the local language. I would not expect if I lived in France everybody around me to learn English, I would have to learn French if I wanted to get along.
Your question, however, goes beyond just language. The question is really how much do we as citizens of this country expect others to adapt to our ways. In my humble opinion, the term "melting pot" we use to describe ourselves is very apt. We can take traits, traditions and customs from others and make them our own. For instance, I have a friend who lives in California, born and raised as WASP as they come. He chooses to adopt some facets the lifestyle of a Japanese person, to the point that his Japanese is more fluent than many native Japanese speakers. He sleeps on a mat on the floor, his home is very spartan, to the point of austere. Yet, when he visited there, he said he could never live there because there were many things culturally and socially he did not like. Anyway, while we may not like or understand certain customs of another culture, we are on the whole enriched by learning of them and embracing them (as long as they are not illegal, immoral or unethical).
In short, we as a people should demand certain things from all people who choose to live here, such as paying taxes, jury duty, getting necessary documents (driver's license, etc.) and be able to communicate on some basic level with those around us, while leaving other things to the choice of the person.