It has little to do with survey design. Fact is, Americans have a poor cultural history of personal savings.
Though notably, people do draw a distinction between "saving" and "investing." Most middle-class Americans will have some form of "investments" like a 401(k) or a 403(b), individual IRAs, other forms of pensions, etc. While I would consider this to be a form of savings, these reserves are typically the last to be drained. "Savings" are typically cash savings, or some other form of liquid assets.
But living paycheck to paycheck isn't necessarily the implication that you have no savings of any kind. Rather, the concept is more about how little wiggle-room there is in standard household budgets. However, I would argue that tight budgets are a function of poor fiscal discipline, rather than "difficulty". Americans love to moan about how hard life is (and indeed, it's not easy), but most Americans have never been outside of the country, or have any idea how hard life is in other countries.
