You can protect your whole Posterous site with a password. See the Privacy section by clicking Settings in the action dropdown from the Spaces section.

Be sure to save your settings by clicking Save Settings at the bottom of your page.
You can also set a seperate password for your Space. After you set a password, everyone visiting your site for the first time will be asked to input the password you selected to view the Space. Your visitors can set their browser to remember the password for subsequent visits. If you would like to reset this automatic site access for returning visitors, click Reset site access.