I heard that the Bet HaLevi and the Peri Megadim hold that there is no Mitzva for a person to don Tefilin everyday. Can someone source these opinions and explain exactly what they are meaning to say?
I always understood that they mean to say that the mitzva is to have them on always and there is no difference if you wear it for 1 hour today and 1 hour tomorrow or two hours today and none tomorrow. Each second is its own individual mitzva independent of what day it is on. It is actually kind of hard to justify why each date should matter.
Pri Megadim (Eshel Avraham 37:2) discusses whether the obligation is constant or daily.
Rabbeinu Yonah (Iggeres Teshuva Ois 24) writes that one who doesn’t wear tefillin has close to 300 עונשים yearly (excluding Shabbos and Yom Tov etc.), which sounds like one transgresses the commandment for each day one doesn't wear Tefillin.
The Gemara (Menachos 44) writes “he who doesn’t fulfill the obligation of tefillin transgresses eight commandments”. Smag (Asei #3) and Shibolei HaLeket (Inyan Tefillin) are clear that one transgresses these eight commandments daily.
(See Tosfos [Menachos 35b], where a disagreement is presented as to whether one must tie the tefillin daily.)
The Brisker Rav — quoted by Reb Moshe Shternbuch תשובות והנהגות ח”א סי’ מ”ט, ח”ב סי’ ל, ח”ג סי’ י”א — held that the obligation is all day, and that there is nothing different about today than tomorrow. Therefore, not wearing it for a whole day does not constitute a greater deal of bitul (nullification of the commandment) than not wearing it for an hour. See also Moadim Vezmanim.