The log says:
:info:configure nawk: illegal jump type 339
:info:configure input record number 16, file
:info:configure source line number 306
We've seen this problem several times before with other ports. The problem is that you have the nawk port installed, and cgminer tries to find an awk implementation for its configuration, and decides to use nawk, but nawk is not compatible with what the configuration wants to do. If you temporarily deactivate the nawk port, then you should be able to build cgminer. You can re-activate nawk later if you want.
sudo port clean cgminer
sudo port -f deactivate nawk
sudo port install cgminer
sudo port activate nawk
In other ports we've used the conflicts_build portgroup to handle this conflict. Perhaps this could be added to this port as well.