how can i show an “under construction” message and hide the blog?

There are plugins for this. I recommend Maintenance Mode

this is great! although i get an error when i’m logged in:

Fatal error: Cannot redeclare arbitrary_mail_header_base64_encode() (previously declared in /wp-includes/pluggable-functions.php:176) in /wp-includes/pluggable-functions.php on line 176

any idea what’s causing this?

When I upgraded my blog from WP2.0 to wp2.1.2, I simply created an index.html file and put it in the root of my blog directory. Any subsequent visitors would then see a message that I had put in that file — that things were under construction. At the end of my upgrade process, I deleted the file and my blog was back online automatically.

Hope this helps,
Ron

Or rename index.php and put something else in its place..?

To anyone with this problem now in 2008, this plugin will hijack your site. It adds a ton of Meta tags in all of your WordPress files. For more information on what they say, email me at abray918 at yahoo dot com. I know how to fix it. They are basically hijacking and putting a redirect in here. I don’t suggest using it.