I only just started trading the Eurodollar a few weeks ago so I am slowly increasing my size. Also not as much liquidity on globex yet as in Euribor. I really just dabble on CME in the afternoons if there isn't much going on, on LIFFE and I only set myself a personal target of £1k/month for now. Other downside is that they do not pay a rebate like LIFFE do for volume.
I heard today that CME are going to offer a "new trader scheme" offering rebates to traders that have not traded before in order to tempt them into Eurodollar.
Did you know globex have a 100% pro-rata system, unlike LIFFE, so if you pull your orders, go for a dump, and replace them when you get back, you get same priority. This is why it is sometimes necessary to put 100-200lot orders in to get filled on a few and so I imagine the reason bid and offer volumes get huge is because everybody is doing that.