I was thinking about this a bit more. In my first answer, I was talking about what would actually happen if you got rid of money. But the question implies that people are suddenly altruistic ("pool our collective resources"). The problem with this is how you decide who should do what. And it might turn out that the situation posited ("without worrying about who owes whom?") is impossible in principle. Even to keep things going as they are now, someone needs to decide what needs to be done and by whom. Someone needs to decide who should give you the things you need to survive, and how much to give you. All of that implies that someone is saying "A should give X to B" and this is just a way of worrying about who owes whom what.

Assuming everybody does what they are doing now, the situation will remain the same as it is now. In other words, people will still go to their jobs and do their work, the stores will give them stuff, and so on. In practice everything would collapse, for the reasons implied by gjm in his comments. Namely, since the people in the store don't ask me if I have been going to my job, just as they don't do that now, that means I can get away with going to the store and getting stuff, but not going to my job. Or, even if I do go to my job, I can take a lot more stuff from the stores than I'm actually contributing by my work.