How do I activate a "God Mode" cheat in Portal?

According to cheatcc it's not just typing god in the console

Enter the options menu, select "Controls", then "Advanced". Turn on the option for the console. Then while playing the game, press ~ to display the console window. Type "sv_cheats 1" to enable cheat mode. Then, type one of the following codes and press [Enter] at the console window to activate the corresponding cheat function:

according to the link, God Mode is just god. there is also buddha which allows you to take damage but not die.

Keep in mind though that some hazards such as the toxic water, you dying in meant to help you get out as if you could survive in the toxic water in some levels, you would be suck and unable to get out. you may be able to get around this by using sv_gravity [number] which changes gravity with 600 being the default