I have found a way to make this work with launchd. This requires two steps: First creating a script that downloads the webcam picture, and second creating a LaunchAgent plist file that will call the script every so often.

This method will update the background picture of a specific Space, but only while you are on that space (also, when logging in and maybe when waking from sleep).

First step: Creating a script that downloads the picture and changes the desktop background

1. Create a folder, e.g. ~/Library/Desktop Pictures/Webcam.
2. Select that folder to be your desktop backgrounds folder in System Preferences → Destkop & Screen Saver.

3. Write a text file with the following content:

   #!/bin/bash
   shopt -s extglob # required for fancy rm
   # This script updates the desktop background of a specific Space to a webcam picture
   # while you are currently on that space.
   #
   # Choose a webcam:
   
   remotepic=http://www.foto-webcam.org/webcam/wallberg/current/full.jpg
   
   # Choose a desktop backgrounds pictures folder of the Space where you want to see the webcam
   # (you have to set this manually in System Preferences → Destkop & Screen Saver):
   
   webcampicturefolder=~/Library/Desktop\ Pictures/Webcam
   
   # check the desktop background pictures folder of the current Space
   currentpicturefolder=`osascript -e "tell application \"System Events\" to get pictures folder of current desktop"`
   # only proceed if you are currently on the space where you want to see the webcam
   if [ "$currentpicturefolder" == "$webcampicturefolder" ] ; then
     localpic="$webcampicturefolder"/$(date +%Y%m%dT%H%M%S).jpg
     backup="$webcampicturefolder"/backup.jpg
     #remove all but the previous backup file and txt files:
     rm "$webcampicturefolder"/!(*txt|`basename "$backup"`) 2>>/dev/null
     # get the new picture unless there is a connection failure (-f flag):
     curl -fs -o "$localpic" "$remotepic"
     # make a backup of the new picture:
     cp "$localpic" "$backup" 2>>/dev/null
     # if no new picture has been downloaded, copy from backup:
     cp "$backup" "$localpic"
     # see http://www.macosxautomation.com/applescript/features/system-prefs.html
     osascript -e "
     tell application \"System Events\"
       tell current desktop
         set picture rotation to 0
         set picture to POSIX file \"$localpic\"
       end tell
     end tell
     "
   fi
   

4. Save the file, e.g. as ~/Library/Desktop Pictures/Webcam/getwebcam.sh

5. Make it executable by issuing the following command in the Terminal:

   chmod u+x ~/Library/Desktop Pictures/Webcam/getwebcam.sh
   

Second step: Creating a LaunchAgent plist that calls the script

1. Write a text file with the following content. You need to adapt the string /Users/myusername/Library/Desktop Pictures/Webcam/getwebcam.sh so it points to the script created in the first step. You cannot use a relative path with ~. Change the dict elements with the "Minute" key as you see fit – you can add more of them. The integer determines at which minute of every hour the script will be called (see also man launchd.plist on your Terminal).

   <?xml version="1.0" encoding="UTF-8"?>
   <!DOCTYPE plist PUBLIC "-//Apple Computer//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
   <plist version="1.0">
   <dict>
     <key>Label</key>
     <string>me.myname.update-desktop-from-webcam</string>
     <key>ProgramArguments</key>
     <array>
       <string>/Users/myusername/Library/Desktop Pictures/Webcam/getwebcam.sh</string>
     </array>
     <key>RunAtLoad</key>
     <true/>
     <key>StartCalendarInterval</key>
     <array>
       <dict>
         <key>Minute</key>
         <integer>01</integer>
       </dict>
       <dict>
         <key>Minute</key>
         <integer>16</integer>
       </dict>
       <dict>
         <key>Minute</key>
         <integer>31</integer>
       </dict>
       <dict>
         <key>Minute</key>
         <integer>46</integer>
       </dict>
     </array>
   </dict>
   </plist>
   

2. Save the text file to ~/Library/LaunchAgents/me.myname.update-desktop-from-webcam.plist – the name should match the "Label" key in the file.

3. Load it by issuing the following command:

   launchctl load ~/Library/LaunchAgents/me.myname.update-desktop-from-webcam.plist