I'm aware that you addressed varying lifestyles, but I think 'average American lifestyle' isn't something you can arrive at. People are just gonna fill in the blanks with what comes to mind (like Odo's 'guns and bravado'). I've lived in very rural Texas and very urban Texas and I'm reasonably certain that you can't average the two experiences together into suburban Texas. And America is a large landmass with a significant population spread out across it (even if the coasts are more populous). There are too many variables just running amok for me to definitively make a broad generalization about Americans. A lot of a person's day-to-day existence (and thus stress levels) is just geographically and local-culture based.
Speaking of that word, if we're talking about what we'd refer to as an American culture - what we all have that's pretty much the same wherever you are - like what Odo mentioned - the Information Age
has aided and abetted that. It's a lot easier to focus on keeping up with the Joneses when they're tweeting pictures of their lunch. Of course that phrase was, at least
according to Wikipedia, in the vernacular at the start of the century (err, the one before this one - I'm saying it was in 1913). So this was no doubt a source of stress and anxiety to at least our great grandparents as well.
This is all a long-winded way of saying that we like to assume our time and our culture is some kind of key turning point in history (which is definitively impossible for us to actually know).
To answer the original question at the end of your post, we've been dealing with a recession, the nearly ubiquitous rise of the Internet, and a nation obsessed with security, and that's just been this past
decade. That seems like a good reason for anxiety and depression rates to rise, and prior to that we've had a steadily improving awareness of mental health (and even further back an increasing basic understanding thereof).
The
TL;DR of my opinion is that the rates of extant cases of depression and anxiety fluctuate around a sort of baseline, and if 'American lifestyle' means 'modern American culture', it's probably caused a significant spike in that. But I think the majority of diagnoses are because people are more willing to admit they have a problem and there are more ways for them to deal with that problem than in the past.