I just had the same issue on my install 4th March 2011 on Speedster 2.0.6 and Magento version 188.8.131.52.
I am looking into this now. I notice this is a very recent version of the Speedster software. I will try looking through the code to find the source of the error and failing that I will get the key to install the previous version 2.0.5. (which I assume is more stable!)
My error currently is:
Downloading Fooman_Speedster-2.0.6.tgz ...
Starting to download Fooman_Speedster-2.0.6.tgz (68,007 bytes)
. . . . . . . . . . . . . . ...done: 68,007 bytes
Could not chmod /home/perfects/public_html/nju/lib/minify/.tmp.htaccess to 666 chmod() [function.chmod]: No such file or directory
ERROR: commit failed