Golang's use of a potentially unbounded number of threads is just insane. I used to be fairly bullish on golang, but this, combined with the fact that its garbage collected, makes me feel its just unsuitable for production use.
Goroutines are actually better AFAIK because they distribute work on a thread pool that can be much smaller than the number of active goroutines.
If my quick skim created a correct understanding, then the problem here looks more like architecture. Put simply: does the memcached client really require a new TCP connection for every lookup? I would think you would pool those connections just like you would a typical database and keep them around for approximately forever. Then they wouldn't have spammed memcache with so many connections in the first place...
(edit: ah, it looks like they do use a pool, but perhaps the pool does not have a bounded upper size, which is its own kind of fail.)