The Rishonim all ask – this seems like it is a shaas hashemad, so shouldn’t one have to be moser nefesh for anything even not the big three – as the gemara states in Sanhedrin, even arakta demasana – the tying of the shoelace? Tosfos limits the ruling of arakta demasana to be something that is making you dress not like a Jew, while not wearing tefilin is different, since many Jews don’t wear tefilin all day so you won’t look like a goy. The Ramban and others formulate the difference as follows – tefillin is an aseh, so for bittul aseh we do not have to be moser nefesh, since שב ואל תעשה שאני. This leads to a different question, if he did not have to be moser nefesh, why did he take a chance in the first place and wear them? (Similar to the famous question on Mordechai why he risked his and Am Yisrael’s life not bowing to Haman).
This question leads to the BIG machlokes if one is allowed to give up their life optionally (not the big three and not shaas hashemad). The Rambam (יסודי התורה ה:ד) rules that one cannot do so as he writes: כל מי שנאמר בו יעבור ואל יהרג ונהרג ולא עבר הרי זה מתחייב בנפשו. The Lechem Mishneh asks from our case to this halacha and therefore rejects the ideas suggested above (aseh is different or based on how you look), However, he says that Elisha was able to take off his tefillin once he did the mitzva of wearing tefillin that day.
Other Rishonim use this case among others as proof that one may decide to give their lives. The Ran (based on the Ramban) writes (on the Rif in our sugya) “שאע”פ שאינו מחויב ליהרג על קיומיה אפ”ה רשאי למסור נפשו עליה ומקבל שכר שכל מצוה שמסרו ישראל נפשם עליה בשעת הגזירה מוחזקת בידם ומקבלין עליה שכר הרבה ….”
For an interesting listen on this (related to Holocaust responsa: http://www.yutorah.org/lectures/lecture.cfm/728723/Rabbi_Aaron_Rakeffet-Rothkoff/2008-11-02_Responsa_06, about halfway through the shiur