It is brought in the Gemara (Pesachim 53b): "Tuddus of Rome expounded: What did Chananiah, Mishael, and Azariah see that made them surrender themselves to the fiery furnace for the sanctification of God's name? They reasoned a fortiori from the frogs. If the frogs, who are not commanded concerning the sanctification of God's name, it is written about them 'and they shall come up and go into your house [etc.] and into your ovens and into your kneading troughs.' When are kneading troughs found near the oven? You must say, when the oven is hot. Then we, who are commanded concerning the sanctification of God's name, all the more so."

Now, there are several questions about these words of the Gemara:

Firstly, the Maharsha's question in Chiddushei Aggadot there, his words are: "However, this a fortiori reasoning is flawed, because the frogs, although they were not commanded concerning the sanctification of God's name, nevertheless sanctified God's name since they were not commanded 'and live by them, etc.' But Chananiah and his companions, although they were commanded concerning the sanctification of God's name in public, nevertheless, here in private where they were not commanded concerning the sanctification of God's name, they should not have surrendered themselves since they were commanded 'and live by them, etc.'" Meaning, one could refute the a fortiori argument and say that we cannot learn self-sacrifice from the frogs, since it might be that it was specifically imposed upon them because there was no contradiction to another obligation, as they were not commanded 'and live by them.' But for a person who is commanded 'and live by them,' and self-sacrifice contradicts this obligation, it is not imposed to surrender.

Another question concerning this matter is raised by the Sha'agat Aryeh (brought in the book Peninim Mishulchan HaGra), which is: What proof did Chananiah, Mishael, and Azariah bring from the frogs, for they were explicitly commanded in this matter by God's statement to Pharaoh through Moshe 'and they shall come up and go [etc.] into your ovens'?

Another issue is the Tosafot's question (Pesachim there, s.v. Ma), where they ask, why did Chananiah, Mishael, and Azariah need to learn this a fortiori from the frogs, for the obligation of "be killed and do not transgress" concerning idolatry is well-known and famous, as stated in Sanhedrin (74a), that everyone agrees that in public one must surrender oneself even for a minor commandment. Tosafot answer that Nebuchadnezzar's statue was not actual idolatry but a statue he made for his own honor, and the obligation of "be killed and do not transgress" did not apply to bowing to it.