Having an identity card is not that big of a deal. Plenty of people already have identity cards--driver's licenses or state identity cards--and carry them with them wherever they go. It takes very little effort, and quickly becomes second nature to carry these cards in a wallet or purse. While what it implies to carry a card may be controversial (such as the law checking them for illegal immigrants), the actual process of having required identity cards would not be difficult to implement. In fact, it can also be a safety feature in case someone is injured and unable to speak or remember who they are.
Most states and countries require adults to have some form of identifiication. Drivers' licenses, passports, county ID's already exist. In the US, resident aliens are required to have identification stating their status. We need ID for healthcare, to drive and often to work. Citizens and non- citizens should not be treated differently in terms of ID requirements, and governments should not require citizens to carry additional forms of identification.