After the installation, even before the very first "updating Steam" dialog appears, Steam is fully installed. You can re-run it by launching it normally, and you can run it by just launching it again. The it will try to update again.
Sometimes the local Steam servers are down, and updating fails for a while. Usually the problem goes away when trying the next day. The Steam version in the downloadable installer also has some updating bugs. Those were fixed in later Steam versions, but it is hard to download the update when updating doesn't work. In this case a workaround is to copy a Steam installation directory from a Windows machine or another working CrossOver installation.
Please Note: This Forum is for non-application specific questions relating to installation/configuration of CrossOver. All application-specific posts to this Forum will be moved to their appropriate Compatibility Center Forum.
CrossOver Forums: the place to discuss running Windows applications on Mac and Linux
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