Use ssh and pipe the tarball to your local machine:
It will work better if you use pubkey authentication and run ssh-agent & ssh-add before hand so you aren't prompted for a passphrase from ssh.
ssh user@host 'tar -C /var/www/html/ -cZvf - . | cat >/root/Desktop/html06082011.tar.gz
However, I'd recommend ssh'ing as a regular user and never running an X desktop as root.
You could also ssh to the server first and ssh back to the client stream the archive.