Mondo Agency/WMG

The President is vital to the characters as a plot point
The Boss wishes to protect the President because their world will end without him. After the President dies, the game ends. There is no sequel, so this is essentially killing the Boss and the entire Agency. The person planning to murder the President is cactus, and the Boss wants to prevent that. Note that, by making a game where the only choice is to kill the President, cactus is basically forcing it to happen, and assassinating the President himself. The only way to successfully foil his plot is to not play the game.


 * OH MY GOD THAT ACTUALLY MAKES SENSE!

Agency is the "prequel" to Mondo Medicals
The "Terminal Illness" is actually the "cancer" mentioned in Medicals, and the unfortunate victim of it is the Agent's father. After being fired, the Agent goes into a Heroic BSOD, and starts work on "cancer research".

Agency is the "sequel" to Mondo Medicals
The "Cancer Research" program in the first game was being sponsered by the government. The Agent in the second game is the brother? of the protaginist of the first game, and after he hears what happened to him, he sets out to get revenge on the corrupt government responsible.

The world of Mondo is a very low-tech Matrix
And the "natives" are actually viruses (i.e., they are native to this fake world, with no human counterpart like the TV-headed people -- note that they are 2D sprites in an otherwise 3D world). "We built a world, and the natives will destroy it!" Unrelated to this, the assassination of the President was carefully orchestrated by some kind of resistance movement working within the Agency, carefully constructed to look like it was the fault of a rogue agent. (The Agency may also have the ability to control the makeup of the world to some extent; hence the buttons and the inability to do anything but use them. See also the plot twist in BioShock (series).)
 * Possibly supporting this, consider that after killing the freaking President, all you get is fired. Clearly the Agency isn't too broken up over this, if you know what I mean.