Does doing poorly in a course hurt my chances of getting into grad school? I'm a chemistry major and I've developed a strong interest in some areas of physical chemistry (and physics) and I do really well in physics and math courses. However, organic chemistry has really hit my GPA pretty hard.

This is due mostly to the fact that I'm having a tough time with the subject material and recent illness. Aside from being sick, I've been doing well in my other classes (so the blame is really shifted more toward the I'm-not-"getting"-organic) aside from receiving a handful of W's which I know will also hurt.

Since Organic chemistry is definitely a course within my major, I'm worried that it will significantly damage my chances of getting into grad school. I got a C- in the first semester of Organic and an F in the second semester.

I retook Organic I and got a B. I'm retaking Organic II and I'm doing much better, but the initial try will still appear on my transcript.

If I want to pursue physical chemistry, how awful are my organic grades and my Ws going to look to admissions?

(Note: My GPA was pretty awesome before Organic and I'm doing well in my other classes.)

I would graduate with roughly a 3.6 GPA. Other than Organic, I fare well in my courses. I have done undergraduate research and have presented several times and will likely have a paper before I graduate.

Edit: In the time since I've written this, I retook both Organic I and II and attained a B in both classes.
I am a tenured associate professor in the mathematics (note: not chemistry) at UGA and did graduate admissions for several years there.  

I am a little surprised that the two answers so far have avoided the obvious: getting a C- grade in two required courses in your major certainly has a negative effect on your chances of getting into graduate school.  The only question is how much.  I don't want to speculate on this because you deserve answers from my opposite number in a chemistry department, and I hope you'll get one.  I'll just say: if we "transposed" this question into mathematics, getting C- grades in two core courses that are well known to be difficult enough to knock some students out of the major (say, real analysis): that would indeed be a serious flaw.  We can admit students who got good grades in all the key courses, and we usually do.

However, I don't think you have asked exactly the right question.  The issue is not whether you should abandon your graduate school plans based upon your performance in one (or two) courses.  You shouldn't.  But trying to precisely quantify the damage is our job, not yours.  Your job is to avoid if possible, and if not possible remedy, the problem.

For a very serious student (students who want to go to grad school should count as "very serious"!), getting a C- in a course and then moving on to take the continuation course with the expectation of more of the same is a tactical error.  You say you plan to retake the courses anyway.  Then why are you even taking the second course now?!?  You need to plan more precisely for your own success.  I would look into withdrawing from the second semester course if it's at all possible.  

You also mention health problems.  They can certainly affect your academic and professional performance, and this can happen in an uneven way.  It is quite plausible that you're doing as well in the other courses that you have more talent / experience with / predilection for as you would have done if you were healthy and doing much worse in the course that needs more of your time and energy.  Really consider taking time off, or adding a semester or a year, or doing whatever you can to lighten your load and give yourself the chance to do well.  It is much easier to get official accommodations for serious problems while they're occurring than to try to explain two years later the dip in your transcript.  

In general I think you could get better advice on which courses to take when and how to succeed in your major.  A lot of the most successful students are successful not because of superior talent but because they've been properly mentored or set up for success by others, or because they instinctively know much better than others how to set themselves up for success (which, contrary to what I said above, is certainly a talent).  

Good luck.