In a sense, I don't think most people's happiness is limited by money. Surely the lack of money can bring unhappiness, but I think generally the middle class is happy, and has been for the recent past (just for the sake of argument, the last 3-4 generations).
Maybe my definition of "middle class" is wrong? To me, the "middle class" encompasses the people who still have to work a job, but are able to pay all of their bills in a timely fashion, save some money, and generally support themselves and their dependents. Lower class would mean people living paycheck-to-paycheck or maybe slightly below: just existing means going backwards. Upper class would mean essentially people whose wealth means they can choose to work or not work, and can essentially afford any needs & wants regardless of hours-worked.
Don't we have that already? Comparing the present-day to a generation or two ago, incomes and quality-of-life have changed, but the "middle class" is still the middle class. Two generations ago, having 2 television sets, 2+ cars per household, phones for each person (child or adult), trips overseas, eating foods from all over the world, etc. meant upper class (or quite close to it). Nowadays I'm guessing(!) most families have more than one car, everyone has a cell phone, people travel the world, eat foods from various cultures regularly and go to college more than ever before.
But there's still a notion of "middle class", and always will be. The current "middle class" lives fairly close to the "upper class" of a few generations ago in a lot of ways. Why that is is up for debate (lack of savings? lower wages? Could be a lot of things), but overall I'd say based purely on lifestyle, our current middle class has the cultural habits of the upper class of a few generations ago.