People usually have an affinity to exaggerate. Stock exchanges are the prime example. News on a company may make the stock price to increase very rapidly, only to see a while later for the opposite to take place. Similarly, humans put a lot of emphasis on recent news. This effect can also be observed when someone is telling a story in a social situation. Usually, to get other people interested, the story-teller would twist the statistics or exaggerate the story to a level that people would find interesting to listen to. This is very common in many cultures and there are many aphorisms reflecting the concept. Equally, if there is a problem, it is made to look more important than what it is and sometimes it is so much exaggerated that may make you feel that the end of the world is coming.
However, as bad as this may sound, it is sometimes important to do so as you can get the attention of people who may otherwise not be interested or have no time for such things. For example, it is perfectly reasonable to exaggerate on global warming since it is an important issue that needs to be addressed and that there is a lot of reluctance and laziness in doing anything about it. In short, you need to big it up.
In Risk, you can also pick up an issue and big it up. Make an issue, the biggest problem there is and players will start listening to you and come to your rescue. All you have to do is to slightly exaggerate the problem’s effects on the game and expand it. You can use slippery slope arguments to deceive players into thinking that a cascade of events is indeed inevitable. The end of the world (or in this case, the end of the game) is coming and that if they want to be around when this happens, they need to do something about it now: and your solution is the only way to address it. Make sure you make it clear how your plan may benefit them in the long run. As stated earlier, if you want others to listen to you, make it personal for them and show them how your scheme may benefit their life.