That's a big problem with means testing of public benefits. If one sets the bar very low, then a lot of lower-middle-class people won't qualify. So that is why a lot of lower-middle-class people resent welfare benefits - they earn too little to live very comfortably, and too much to qualify for welfare.
That is what the advocates of Universal Basic Income hope to avoid, by avoiding such low-bar means testing, even if it means giving aid to people who might seem like they don't really need it. That's why Social Security and Medicare are successful, for instance.
