The thought of having to carry an identification card may be upsetting to some, but the truth is that many adults already carry some form of ID, such as a driver's license or state ID card. The government could potentially abuse asking for IDs if they were required, but if it ever came down to a need due to illegal immigration, terrorism, or some other threat, I would be someone who would be willing to be carded.
People already look at government as too intrusive and I believe they would object strenuously to a government issued ID card. That is compounded by the problem of older people who have no birth certificates or forms of ID that could be used to show who they are. There are already many who are disenfranchised from voting because of this problem with lack of identification.