I suspect Mr. Aso is going to claim his remark was taken totally out of context.
From Nikkei Shinbun, quoting Kyodo News (7/30/2013):
Taro Aso, Vice Prime Minister and Finance Minister, gave a lecture in Tokyo in the evening of July 29. Regarding the revision of the Japanese Constitution, Mr. Aso referred to the Nazis Germany before the World War II and said, "The constitution of Germany's Weimar Republic [the Weimar Constitution] was changed unnoticed. It was changed before anyone was aware. We could learn from that technique." He also said, "[Change of the Japanese Constitution] shouldn't be decided in turmoil", and his remark [about Nazi Germany and Weimar Republic Constitution] was in the context that the changing the Constitution should be discussed in a calm environment.
According to wiki, the Weimar Constitution "technically remained in effect throughout the existence of the Third Reich from 1933 to 1945":
Hitler's subversion of the Weimar Constitution
Less than a month after Adolf Hitler’s appointment as chancellor in 1933, the Reichstag Fire Decree invoked Article 48 of the Weimar Constitution, suspending several constitutional protections on civil rights. The articles affected were 114 (habeas corpus), 115 (inviolability of residence), 117 (correspondence privacy), 118 (freedom of expression /censorship), 123 (assembly), 124 (associations), and 153 (expropriation).
The subsequent Enabling Act, passed by the Reichstag on March 23, 1933, stated that, in addition to the traditional method of the Reichstag passing legislation, the Reich government could also pass legislation. It further stated that the powers of the Reichstag, Reichsrat and Reich President were not affected. The normal legislative procedures outlined in Articles 68 to 77 of the constitution did not apply to legislation promulgated by the Reich government.
The Enabling Act was effectively a constitutional amendment because of the foregoing alterations to the normal legislative process. The act met the constitutional requirements (two-thirds of the Reichstag's members were present, and two-thirds of the members present voted in favor of the measure). The Act did not explicitly amend the Weimar Constitution, but there was explicit mention to the fact that the procedure sufficient for constitutional reform was followed. The constitution of 1919 was never formally repealed, but the Enabling Act meant that all its other provisions were a dead letter.
Two, and possibly three, of the penultimate acts Hitler took to consolidate his power in 1934 actually violated the Enabling Act. Article 2 of the act stated that
'Laws enacted by the government of the Reich may deviate from the constitution as long as they do not affect the institutions of the Reichstag and the Reichsrat. The rights of the President remain undisturbed.'
However, on 14 February, the Reichsrat was abolished even though Article 2 explicitly protected the existence of that body. It can be argued that the Enabling Act had been breached two weeks earlier on 30 January, when the Law for the Reconstruction of the Reich transferred the states' powers to the Reich and rendered the Reichstat obsolete. Hindenburg died on 2 August, and Hitler appropriated the president's powers for himself in accordance with a law passed the previous day. However, in 1932 the constitution had been amended to make the president of the High Court of Justice, not the chancellor, acting president pending new elections. Nonetheless, the Enabling Act did not specify any recourse that could be taken if the chancellor violated Article 2, and no judicial challenge was ever mounted.
Instead of referring to Weimar Republic, Aso could have referred to Japan's ally the United States. The surveillance state under NSA is not exactly what the country fought the war of independence against England for, but here it is, before anyone is fully aware, the Constitution has been subverted, or for pro-NSA surveillance people, "updated" to meet the needs of modern times.
I may also add that Mr. Aso wants to become Prime Minister again, just like Mr. Abe has done. He thinks Abe's health problems will get him again sooner or later.