The AP offers an account of the speech, as well as responses from several protesters, none of whom seems to have been swayed by Dilma's words.
While Dilma has enjoyed extremely high approval ratings, the protests could change public sentiment and might make it easier for a challenger to offer her real competition in the 2014 Presidential election.
As the article points out, even Dilma's critics (which includes most of the Brazilian press, who have never been big fans), acknowledged "the difficult situation facing a government trying to understand a mass movement with no central leaders and a flood of demands."
It seems clear that the protests are not going to die out any time soon, and Brazilian politicians, unaccustomed to such massive demonstrations, are simply not prepared to deal with them.
Dilma herself waited an unusually long time before issuing any statement at all, and her initial response was brief and non-committal. By last Tuesday, she had acknowledged that the protests were a legitimate part of the democratic process, but the fact that she waited almost two full weeks before speaking to the nation on TV says a lot.