26GB of space isn't very much space for an OS upgrade.
The Mavericks download is 5.29GB. It will create some more files to allow the installer to boot. That leaves you with about 10-20GB to replace the entire OS.
The specs only want 8GB of free space, but I think they will need some free space too. (http://www.apple.com/osx/specs/)
10.9 should be smaller than 10.6, but why risk a failed install on the machine? Is it all backed up?
I'd backup (twice), delete or archive old files so there is at least 40GB free.
Also if the error reappears make a note of the actual package that is failing (assuming the dialog says) otherwise we simply have to guess.