The "stresses" come from trying to maintain a middle-class lifestyle on a lower-class income.
As someone who once spent a considerable amount of time (just over a decade) supporting myself on a just-above poverty line income, I notice that a lot of people talking about the impossibility of living on minimum wage are implicitly assuming that everyone must conform to certain cultural norms (living alone, owning and maintaining a car, going out to eat or for entertainment, etc). Many of the financial stresses of low income are moderated by not conforming to those norms.
For example, take this story: http://www.forbes.com/sites/laurashin/2013/07/18/why-mcdonal...
A major criticism of the McDonald's budget is that it only allocates $600 per month for rent. Ok, well, I'll grant you that it's hard to find a single-bedroom apartment in most major cities for that little. However, it is quite easy (I know, because I have done it) to find a two bedroom apartment in a nice, safe neighborhood in Los Angeles (of all places) for about double that. Living with roommates may not be everyone's ideal (some prefer it), but I find it disingenuous to assume that everyone ought be living in some culturally-defined way. Living with (a) roommate(s) is just one example of a "lifestyle sacrifice" that does not harm your health or safety, and doesn't affect your autonomy as a person (much). But it does significantly reduce living expenses.
Another example is car ownership. Even Los Angeles' "famously bad" bus network will take you anywhere in the county (and there is Zip Car for when it's absolutely necessary to drive). Resisting social pressure (from friends and potential mates) to own a car reduces living expenses dramatically. Some people will look down on you for not having one, but who cares what they think?