Sure, it isn't easy, but they get ID because they need it for damn near everything. For example, you mentioned "work hours". If they are legally working, they have ID. If they get any sort of welfare, they have ID. If they smoke or drink, they have ID.
“Lower-income individuals are less likely to have photo ID. Twelve percent of adults living in a household with less than $25,000 annual income lack photo ID, compared to just 2 percent in households with over $150,000 annual income.”
From http://www.projectvote.org/wp-content/uploads/2015/06/AMERIC...
It is assumed that the people claiming to be Americans without ID are in fact Americans without ID. It's kind of hard to verify this without ID, eh? The given percentages are in the ballpark for estimates of illegal aliens, meaning that these might be people who aren't supposed to have an American ID and in fact aren't supposed to vote.
The ID law has been shown to be slanted to disfavor the working poor who vote for one party over another. It's not done as a legitimate concern over fraud; its a political maneuver to favor one party over the other and disenfranchise the poor. That's the argument