This campaign seems to be less about them trying to really understand and empathize with the poor (though it did some of that surely), as it is to raise awareness of the draconian Republican cuts to the program and how unreasonable they are. Again, it is people using their privilege and positions of power to draw attention to difficult daily living situations of those with less privilege.
It's frustrating to me that this gets so much more attention than real poor people figuring out how to scrape by on $4.50 for food a day, but hey, if it works, I guess I'm ok with it. Though it seems like the politician's experiences of trying to do this don't open space for the voices of people really in this situation, but perhaps drown them out. But then, I'm not sure what mainstream coverage has been like (not much in print, but maybe tv?) - but wow, the twitter tag #SNAPchallenge includes a LOT of right wingers saying they eat on much less than that easily and why are they paying for pathetic poor people. Very nasty stuff.
These sorts of actions are hardly new, though perhaps politicians taking them up is. There is a book entitled 'Place at the Table: 40 days of solidarity with the poor' that gives you practical and theological guidance on how to 'eat like the poor' and donate the difference to charity (not solidarity!) It comes from a very Christian perspective. One danger is that these sorts of actions can come across as patronizing and essentialize 'the poor', though I'm not saying that's necessarily the case with either the Congressional campaign or this book (which I haven't read).