Well, we are very happy as a family of 6 living in about 3k sq ft. But, I think as long as we could keep the 3-car garage for storage, we could be comfortable in about 1800 sq ft. We really don't need all this space, at this point, but I won't lie and say it isn't nice. My kids are still fairly young, and much prefer to sleep together rather than in their own rooms, but I imagine as they get older, having their own space will be a good thing.
In the past, we have lived in much smaller homes (apartments). Before moving here, we were in about 1k sq ft, 3 bed/2 bath apartment on the 2nd floor. I wouldn't say we were unhappy, but it was far from ideal with four small children. If we had had a backyard, that would have made all the difference (I see that now, as we have 1/2 an acre for them to run around, dig, ride bikes, etc). I will say, that I was extremely unhappy living in about 700 sq. ft when we had 3 children (and I was pregnant). It probably had more to do with the condition/location of the apartment plus the rest of the things going on in our life, than the actual space - but still, I really, really, could not make the best of it at that point and I'm still bitter thinking about living there now. (not having two vehicles, I'll admit, was a HUGE source of my frustration, on top of other lifestyle struggles.)
Basically, I think having enough space is nice, but not necessarily the determining factor of happiness. It contributes/takes away from it, though, definitely. And again, where that living space is, probably plays a bigger role. My bro and soon-to-be SIL live in a tiny apt in the village of Manhattan. They are very happy - but look where they live, and they don't have children and all their belongings to contend with. Which reminds me (and others have mentioned this), having a ton of stuff in a smaller space (or a big one, actually) can be the difference between making it work, and being frustrated and feeling cramped. I know in the past we could have gotten rid of a lot of non-essentials, and I would have felt just a little bit better about our living space. Also, being able to put up shelving, etc (hard when renting an apt) and making the best use of your space, makes it easier to manage and keep organized.