You posit two questions: one in the title, and the other in the text. They are completely different questions. But to your intention or not, that may mislead readers to the impression that they are the same question.
Did Taro Aso say that Japan should emulate the Nazis in amending the constitution?
Yes, he did. He said that we can learn from the technique that Nazi used to gain popularity from the German people to change the constitution. (There is no doubt that the way Hitler and Goebbels made their speech was very effective in gaining people's attention and sympathy.)
Was Aso saying that the Nazi change in the constitution was a good thing that Japan should emulate?
No, he did not say that the particular change made to the German constitution by Nazi was good (although the major goal of The Liberal Democratic Party (where Aso belongs) from the time of its establishment has been to change Japan's constitution).
Although Aso is said, according to Nonaka Hiromu, to have made a discriminative comment regarding a particular social class in Japan, there is no particular mentioning that he is a supporter of Nazi's policy.
Edit Since there was a request for a source citation, here you go for the whole transcription: http://www.asahi.com/politics/update/0801/TKY201307310772.html