I would imagine most GMs have day jobs. Certainly, I'm yet to convince my players to pay my food and rent in exchange for trying to kill their characters each week. Over the years, I've played games on a Saturday afternoon / evening and always found them a drag as large parts of the only free day a week are consistently lost. For me, the only real option is playing on a week night and this inevitably means a game will sometimes clash with That Day at work. The day you've been hard at it from some stupid time in the morning, with no breaks and no lunch and you're already half asleep when stumbling to meet your group.
Like last night.
So what happens when you're feeling as dead as the zombies the PCs are slaying? Assuming the GM is experienced enough to hold the session together and not accidentally wipe out the party then chances are the worst that will happen is that he will lose control over what is going on.
Control in a roleplaying game is something that needs to be handled extremely delicately. There are entire posts to write about managing player freedom but the short version is that the players should be limited by the world (laws, social norms, etc), their characters (their skillset and the personalities they themselves have created) and their own imaginations - that is it. Mostly, these controls are exercised by the players themselves deciding on their course of action, not the GM limiting them.
The other control is initiative. Who is deciding what will happen next? Are the villains furthering their plans and forcing the PCs to react, or are the players putting their own schemes into play? The answer to this question determines to a certain extent who is controlling the story and will likely move around on a continuous scale over the course of a campaign. Done well (and not in an adversarial way - the players are not the enemy after all) this can be an exciting dynamic to a game as the players steal the initiative from their enemies by doing something clever and unexpected. This is why GMing tired is occasionally not a bad thing. You aren't as on the ball as normal and you're likely to be sitting back a bit and this can firmly hand the players the initiative.
With the players driving, you're likely to see unexpected change. This is not something the GM should fear. If the world is built properly with a rich background and well thought out NPCs with clear motivation (always know the motivation of an NPC if you want your world to make sense) it will survive contact with the players. It may look completely different afterwards, but at least you'll be able to see how and why it has changed and you'll have a good idea how the NPCs will react to it. Massive, unexpected change can be really exciting for the player and the GM and can conjure some of the most memorable moments in a campaign. The capacity for this to happen is a key difference between a roleplaying game and reading a book, or even collaborative storytelling and is something that should be embraced.
In the game last night, with me half asleep, the players had free reign to push their own agendas. As well as freedom from reacting to their enemies, NPCs were more agreeable than they might normally be and newly introduced characters were not as sharp they perhaps should have been. The result? A significant step towards raising an army to oppose an undead horde; creating a political ally who could swing the economic future of the region if handled correctly and making contact with an important source of information who has considerably more mouth than brains. Now, two of these are the result of the player's actions and they were likely to make them happen anyway. The third has (accidentally) introduced a very significant source of intelligence. If they work him properly this could lead the story in a new direction - as a GM this is something I find exciting, but there is no way a character with his personality would have been introduced deliberately.
Fortunately the personality in question is so obnoxious nobody wants to talk to him...