This may not be an issue for all players - if your main opening is already something combative (like a Modern, Alekhine or Sicilian Najdorf) then you can probably play it against everyone. You may even have the opposite problem - that of needing a more solid opening against higher rated opposition!
I, on the other hand, play the French - and a lot of the time I play quite solid lines. This is great against players my own strength or stronger but I have been drawing too many games lately as Black vs lower-rated players.
A few weeks ago I played in the Hastings Masters and I failed to win a single game as Black, despite mostly playing players 200 points or so lower rated than myself. I came close to winning one game before blundering but even there I'd been a little worse from the end of the opening.
Against 1.d4 I don't find this to be so much of a problem - I already play the Leningrad Dutch and this seems to work reasonably well - in fact I may need something more solid against stronger players!
The problem with the French is that there are a lot of 'boring lines' - especially the exchange and variations thereof. Take this recent game for example, played in a local league. My opponent is about 2000 strength but he comes very, very close to getting the draw - probably the only thing that gets me a win in the end is his lack of time...
An interesting endgame at the end but I hope you understand the point I'm making.
With this problem in mind I've been looking a little at the Sicilian recently. I'm experimenting with a few different lines but mostly with the aim to get more interesting and unclear middlegames. I've tried it out a couple of times and here is my most recent game, from just a couple of days ago. My opponent is somewhat stronger than in the previous game (over 2200) but I get the kind of position I'm after.
Obviously with only two games this tells a very one-sided story but I think most people would agree that the Sicilian is somewhat more attacking than the French. Of course there are still some "boring" sidelines, like the Alapin (2.c3) but there are still ways of reaching an interesting middlegame (perhaps trying 2...g6).
Anyway, I'm playing a weekend congress in a few days time and at the time of writing I'm top seed so I'm guaranteed at least a couple of games as Black vs lower rated opposition. Of course it will depend a little what they play vs the French and Sicilian so I can't guarantee I won't stick to the French.
Still, there are lots of good reasons to at least learn a 2nd opening: it makes you harder to prepare against, it leads to different middlegames than the ones you're used to (which helps improve your overall understanding) and also it can help keep you interested in chess rather than just playing the same thing over and over!
I'll let you know how I get on. Let me know in the comments if you also play different openings against players of different strengths!