Believe it or not, until very recently I'd never read any of the Harry Dresden novels. I decided to change that when I realized that I was rather enjoying the Dresden Files game I was in and that I really had very little exposure to urban fantasy. Now, I'm only on the 6th or 7th book, but in the book I'm reading there is a small scene that really cemented the level of danger and seriousness of the coming conflict. The book is all about set up for this event, most of the book is trying to convey how serious it is, and a small half page bit is what actually sells it. It's an important lesson, and something that definitely applies to your game.
So What Was It?
The scene in question involves Harry calling for help to handle a problem. He calls a group of magical trouble shooters, gets one of their head honchos, and when he's maybe four or five words into explaining his problem the person cuts him off with a "we're on our way." That's it. That is the entirety of the scene. It is probably something Jim Butcher did just to show that the group in question isn't always assholes, and to help explain how Dresden is going to come out of this one alive (I presume as there are 14 books in the series.) And yet, had this scene not been there I would not be near as sold on the danger coming.
Why Does This Work?
The reason this works is partially because of setup, but also because of the reaction. A very powerful person is contacted in a world that has a lot of political bull crap going on (even supernatural political bullcrap.) The response? A very important person drops everything to immediately go and respond to this issue. Now, in the scale of things it could seem like an important piece - and presumably this is larger than I currently realize - but at this point in the book I don't know the person being called, I only know the group they represent. A group that isn't too fond of Dresden. The fact that this matter is so big that all that crap gets shelved while a "real" problem can be dealt with? That says a lot.
In Your Game
So how does this apply to your game? Well, partially this is what I was talking about when I talked about Ludonarrative Dissonance. You have all these big things pointing that the big bad is a huge threat, but what about the little things? Do the people care? Are they scared? What about others in the know? If the general attitude of everyone - or even all the key people - in the know is "pfft, you got this" that is going to do a lot to subvert the mood of the game and the building to climax. Even if it is just the small stuff, it can count.
Now, that isn't to say everything has to be pointed in the same direction. Mass Effect (grumble mumble) does a good job of painting a clear picture between politicians and soldiers by how they react to the Reaper threat. While the politicians deny and want to ignore the threat as ludicrous, people who know Shepard trust him/her. Those who only know of Shepard's reputation take a stance closer to "we should take this seriously, even if it could be ludicrous." It does a lot to show the difference between people of action and people of words int he world. It also does a lot to show how far Shepard's reputation has preceded him/her.
The point I want to make is to keep the details in mind when handling things. The famous phrase is that the devil is in the details, and with stories and games this is why. After all, if you keep telling your players they're super powerful badasses but they leave every fight with a handful of HP and wondering how they survived they're not going to feel badass. On the other hand, you give them a lot of easy fights and even a weak group is going to feel like billy badass. Maybe even enough to get in over their head at some point in the future.