When I was 23, I decided to stop doing paid work and try to make a living writing fiction. For about six months I literally starved myself, spending an average $5/week on food (I set up arrangements to get a couple of proper free meals a week - one with my parents, and one in exchange for giving a friend a driving lesson) - making pancakes three times a day from flour, powdered milk and an egg, and frying them in margarine before adding sugar and lemon juice (the sugar and starch made me feel like I was eating a fulfilling meal, and the lemon juice literally saved me from scurvy).
Anytime I needed to go somewhere, I walked - up to two hours. I still have scars from walking until my feet bled. At the time I was young and in good health, and my only "work" was sitting in a comfy chair; I couldn't last a week now, and after a few months I had to concentrate to avoid staggering as I walked. Of course I got sick the second the weather turned cool, and never really got better.
I still spent well over $2 a day due to rent (since I didn't live on the street), contact lenses (I get headaches otherwise, and wasn't willing to suffer unnecessary daily pain), and social obligations - that is, giving people birthday presents (really rubbish ones, too). When people invited me out to dinner, I would make excuses to avoid it, or I'd go and sit with a bunch of people eating delicious food and pretend I was sick, or had already eaten, or was fasting. The worst part of living on so little was trying to stay friends with people - and trying not to hate them for thinking five dollars was no big deal.
I've lived in Indonesia, where things are cheaper, but malnutrition would still be a huge issue at $2/day - and of course you have no safety net, ever. If you get so much as a headache, you can't buy Panadol. If your child is sick, you can't see a doctor - and you couldn't afford the medicine anyway. Your home will be ugly and broken because you can't fix it; your world shrinks to the distance you can walk; and any friend with more money will either pity you, blame you, or carefully forget you exist.
So yes, I can imagine living on $2/day, although "living" is the wrong word. Luckily I don't have to actually live it.
I am not so sure considering the cost of public transport and so many other things . Myki would cost me approximately $6 minimum for a day pass. I can manage when it comes to food. I don't spend on coffee either . There are so many things to consider though when you say $2 a day.. Gas, electricity, toiletries, water bills etc . I think I would need to sit down with a pen and paper and calculate.