Well, you asked several different questions so I'll try to be specific.
1. In response to your thread title, no, I don't think an intelligent person can do anything. It's a nice thought, but sometimes hard work just isn't enough. That's not to say that the hardest things are only achieved by prodigies, just that no one intelligent individual is guaranteed success in any particular venture. Large numbers of very smart people are striving to achieve a certain thing or solve a particular problem, but most of them are doomed to fall short or come up with smart (but wrong) answers. There are just too few positions to be had, and the wrong answers far outnumber the right ones.
2. To the first of your two posted questions, no, genius is not required to master intellectually challenging material or work in a demanding profession. In fact, I would argue that this is where hard work pays off the most! You'll be hard-pressed to find a large number of slackers in high academia -- most of them are passionate, hard-working and subsequently intelligent. But I don't think it's fair to say that they would have been so had they not possessed the drive and work ethic required to learn all they did.
Yes, there are prodigies. There are people who, seemingly without effort, devour the same subjects that 'mere mortals' struggle with. We've all heard of Aristotle, Newton, Leibniz, Euler and Einstein, as well as the more recent men like Witten -- whose historical significance has yet to be determined. But these men are far outnumbered (and outdone) by the countless scientists whose achievements remain largely unknown to the general public in spite of their positive or negative effects.
At most universities there are competent scientists and promising students conducting research which will go largely ignored, save for fellow academics and inquisitive nerds subscribing to scientific journals. But this research will further enlighten mankind, and perhaps even have applications worthy of public recognition. You don't have to be a genius to achieve or contribute. You're surrounded by examples.
3. For your next question, no, "important work" is not solely limited to the brightest few. It is certainly true that the most important things are generally discovered by men of intellect, but that does not mean they were excessively or abnormally intelligent. They were simply smart enough and, dare I say it, "lucky" enough to recognize what was in front of them or infer/intuit what was hidden behind the fog of uncertainty. (I hate to use 'luck', but I was reminded of the saying "The harder I work, the luckier I get.") The most prominent example of this would be Arno Penzias' and Robert Wilson's inadvertent discovery of cosmic background radiation. I recall seeing in an interview that they felt as if they didn't deserve the Nobel, because they saw it as a prize for genius -- their view changed upon further reflection, and the realization that genius was second to discovery. They were being honored for what they achieved, not who they were.
All of that said, I think that most people have a hazy view of intelligence. It is widely and incorrectly assumed that you have to be exceptionally bright to grasp math and science, but only because people overlook the dedicated study that it takes to reach even the most base level of what one might call expertise. So while you may not be intrinsically more intelligent, you are discernibly so by design. You tried to be smart, and so you are. This describes most of us, anyway. The majority. The non-prodigy crowd.
