How do people get along without State ID?
In most states it's not hard, if you live under the radar; that is you don't have a bank account, own property, drive a vehicle, or live as most middle class Americans do. You don't need a photo id to apply for Medicare. Since Medicaid is a state program, that varies with state. In most areas, you can get food stamps with just about any kind of id. In some places a library card is sufficient. For welfare, the type of welfare assistance and state requirements determine the need for ids.
If all Americans were required by law to have a photo id, then it would be reasonable to require one to vote, otherwise I don't think it's a good idea. All states issue voter id cards which can be asked for at the polling place. The source of most voter fraud is disenfranchisement, intimidation, misinformation, misrecording of votes, and absentee voting.