It says in the anime that Rock Lee doesn't have ninjutsu or gen jutsu. Why is that? I've been wondering, everyone has 'chakra', but why can't everyone use it to do ninjutsu and all?
Just because everyone can do such things does not mean people are able to. Lee's situation is not that he can't do it, its that he has absolutely no talent for it. Kind of like Naruto, but worse. However, He does have a talent for Taijutsu, and that is the only reason he was able to become a Ninja at all. Because he is so heavily weighed towards Taijutsu, its the only thing he trains.
His serious lack of any talent what so ever means its not worth his time to train any kind of Ninjutsu or Genjutsu. He would probably spend weeks or months training it, and only get a little progress. Whats worse is that the serious lack of phsyical training he would be doing would to train that would probably weaken him a lot. He would have to increase his already intense training by a lot, and that increase of probably hours a day would net him almost nothing for probably years. For most of that time, he would be training frustrated and depressed due to his lack of progress. At least with Taijutsu, he had hope, but with ninjutsu, he has none.
So, you are probably right, He can do it if he really tried, but it would probably take years for him to do anything substantial, and he would have to overcome hurdles several times bigger than anything he has had to do before, all the while having little hope to drive him. He just doesn't view such a thing as worth his effort. As a Taijutsu master, he can already go against top Jonin and has a decent shot of winning.