Is there a time limit on the Hunger Games?

Question

If a Hunger Games went on for too long - what would happen?

I was looking through the book for an answer and come across this quote:

In two weeks, 23 of you will be dead. One of you will be alive.

But, did Atala just say this as just a figure of speech, or was she was actually implying a time limit?

And it can't go on for ages or it would clash with the timing of the Victory Tour (this is taken place 6 months after each Hunger Games) and could possibly clash with the next Hunger Games too.

The gamemakers could kill off the victors and drive them together, but what would happen if this failed to work and they still didn't kill or attack each other.

Answer 1

No, there is no actual time limit. Further, the scene you reference from the movie does not happen in the book. From the first book's description of the Games (via Katniss, emphasis mine):

The twenty-four tributes will be imprisoned in a vast outdoor arena that could hold anything from a burning desert to a frozen wasteland. Over a period of several weeks, the competitors must fight to the death.

Later, as Katniss is thinking about the kind of environment she will find herself in:

Often there are trees because barren landscapes are dull and the Games resolve too quickly without them.

And, as Katniss and Peeta are holed up, she tries to figure out how long she has been away from home:

How long have I been gone? I'm guessing it's been about two weeks in the arena, and there was that week of preparation in the Capitol.

Lastly, as they are doing the "review show" at the end, it seems this particular games lasted "several weeks":

Condensing several weeks into three hours is quite a feat [...]

So, while I am unsure just how long the 74th Games lasted, there certainly was no two week time frame. We see several times that the Gamemakers will interfere to keep things interesting, so there is no reason to believe that they cannot essentially end it whenever they please.

Plus, they have been known to outright kill tributes in the past:

There was some speculation that the avalanche that finally took Titus out was specifically engineered to ensure the victor was not a lunatic.

Basically, they have (almost) complete control over the entire thing, including the duration.

Answer 2

What would happen if a game went on too long? Tom Doyle has answered his own question - "The gamemakers could kill off the victors and drive them together", as we see done in the first book:

The Hunger Games (book 1), Part II "The Games", Ch. 13:

It’s not hard to follow the Gamemakers’ motivation. There is the Career pack and then there are the rest of us, probably spread far and thin across the arena. This fire is designed to flush us out, to drive us together. It may not be the most original device I’ve seen, but it’s very, very effective.

The second part of the OP's question, "What would happen if this failed to work and they still didn't kill or attack each other"? If, say, the tributes from the outer districts were to team up and kill the highly aggressive inner district tributes, and then just sit down and refuse to fight? The Capitol would, first, execute them, and second, severely punish their families (at least), maybe even everyone in the districts they came from. The tributes' families, friends and people of the districts are the hostages that ensure the tributes put on a good show. While this doesn't seem to be expressly stated, there's enough circumstantial evidence to indicate the Capitol's method of operation.

The Hunger Games (book 1), Part I "The Tributes, Ch. 8:

At first, I expect guards to come for me. But as time passes, it seems less likely. I calm down. They still need a girl tribute from District 12, don’t they? If the Gamemakers want to punish me, they can do it publicly. Wait until I’m in the arena and sic starving wild animals on me. You can bet they’ll make sure I don’t have a bow and arrow to defend myself.

The Hunger Games (book 1), Part I "The Tributes", Ch. 8:

“Do you think they’ll arrest me?” I ask.

“Doubt it. Be a pain to replace you at this stage,” says Haymitch.

“What about my family?” I say. “Will they punish them?”

“Don’t think so. Wouldn’t make much sense. See, they’d have to reveal what happened in the Training Center for it to have any worthwhile effect on the population. People would need to know what you did. But they can’t since it’s secret, so it’d be a waste of effort,” says Haymitch. “More likely they’ll make your life hell in the arena.”

The Hunger Games (book 1), Part III "The Victor", Ch. 21:

I nod because I do understand. About owing. About hating it. I understand that if Thresh wins, he’ll have to go back and face a district that has already broken all the rules to thank me, and he is breaking the rules to thank me, too.

Judging from the general tone of the other questions that people ask, I think there's a very basic misunderstanding about the rules of the games. The "rules" are whatever the Capitol says they are. If the Capitol wants to "break" the "rules", there's no higher authority that can be appealed to.

The Capitol could simply march into the districts, grab two kids at random and shoot them on the spot. They came up with the games as a way to, first, legitimize what is in fact just an execution, and second, display their technological superiority and not just their brute strength.

Answer 3

I deeply apologize for not have very many sources, however I remember them stating in the first book about how the game makers would change the temperatures, (in the first book, they had to deal with crazy temperatures and humidity and then freezing cold, also they included the feast, to speed things up.

From the movie:

Attention tributes, attention! Commencing at sunrise, there will be a feast tomorrow at the Cornucopia. This will be no ordinary occasion. Each of you needs something. Desperately. And we plan to be... generous hosts.

From the book (The Hunger Games, chapter 18):

But occasionally, there will be trumpets followed by an announcement. Usually, this will be a call to a feast. When food is scarce, the Gamemakers will invite the players to a banquet, somewhere known to all like the Cornucopia, as an inducement to gather and fight.

Last among this is that if it takes to long, eventually the place will run out of food, making the tributes die of thirst or starvation.