What are people to read when wearing Tefillin during Mivtzaim:

During Mivtzaim, the people wearing Tefillin are to read all three Parshiyos of Shema.[1] At the very least they must read the first two Parshiyos of Shema.[2] If there is absolutely no time available, the person fulfills his obligation even if he does not say anything at all while wearing it.[3]

__________________________________________________________________

[1] Siddur Admur regarding Rabbeinu Tam

[2] M”A 25/6 in name of Sifri that these two Parshiyos are an obligation; This certainly applies according to those Poskim that rule that all four Parshiyos are an obligation. Now, although if it is already past the time of Shema there is room to learn that they are no longer obligated to say Shema with the Tefillin, as rules Admur 66/11 and Siddur Admur [letter 22 Raskin] and M”A 66/12 that one who is wearing Tefillin after Davening is to say with them a Mizmor. Nevertheless, they are to say it as perhaps this only applies to one who already said Shema without Tefillin due to lack of choice and not to one who is saying Shema for the first time. Furthermore, regarding Rabbeinu Tam Admur in Siddur [and see also Admur 34/5] rules that the custom is to say Shema. Thus initially one should always say Shema when wearing Tefillin. See also Levushei Mordechai 3/5 in name of Maharam Shick 23 that from the Poskim who write one is to recite Shema with Rabbeinu Tam [see footnotes above] it is implied that just like there is Eidus Sheker to recite Shema without Tefillin, so too it is Eidus Sheker to wear Tefillin without saying Shema.

[3] See Halacha 1