I think blarg has the right idea. Personally, I'd bring this up as, "It's getting sort of difficult to buy gifts for everyone, and I think it might be a good idea to come up with some sort of alternative that has us all spending less money per gift, or maybe buying gifts for fewer people. Would you be willing to try out some sort of gift exchange?"
I would approach that conversation with ideas in mind to offer, but I'd ask for ideas from your siblings as well.
In my extended family, because my mom had 3 siblings, there were 8 adults other than my grandparents, and 13 children. There was never a time when any of my aunts or uncles gave gifts to all of their nieces or nephews at Christmas, because that would have been too much. Instead, we had two name draws--one for the grown-ups, and one for the kids. We did it by generation, though, rather than age. Each kid would draw a name, and each grown up would draw a name (that wasn't someone in their immediate family), so everybody both gave and received one gift. My grandparents gave gifts to everyone, and they were the only ones who did.
Eventually, we did away with even that. Now I don't exchange presents with anyone except my immediate family on a regular basis.