I thought I was prepared for immigration, but on my most recent game I received SIXTEEN immigrants in my first batch, which I believe comes at the end of the first winter.
I was able to recover, at least for the time being, because I had expected 8 immigrants and double that was not enough to really push me over the edge, but it was a struggle. I guess I enjoyed it, but receiving a more manageable amount would've been nice.
And it was a total wash when the second immigration brought me up to 54 dwarves. I just gave up at that point, especially because two of them were Nobles and there was absolutely no way for me to manage the influx of normals AS WELL AS the Nobles in a time-frame that kept a lot of dwarves from going crazy.
They did go crazy, and my fortress did fail miserably, and I did have to restart.
I think maybe instituting an immigration cap, regardless of how "prepared" the game thinks the player is, might be a wise move-- or, even better, make three caps, and have them set as "easy", "normal", and "hard" mode.