The Minchas Yitzchak’s explanation of the hava amina to think binyan mikdash might be doche Shabbos or Y”T follows along the same lines suggested by Chaim M. in a comment yesterday. The M. Y. just adds an additional twist which to help explain why the Mechilta illustrates the issur of building the mikdash using a case of fixing the mizbeiach and not with a case of building the actual walls of the mishkan.
As we discussed once before, Tosfos holds that the aseh of Yom Tov is zman gerama and women are obligated only in the lav. This opens the theoretical possibility of saying that the aseh of binyan mishkan could be doche the lav of Yom Tov, as Chaim M. suggested. However, the gemara (Shavuos 15) writes that the mitzvah of binyan mikdash cannot be done at night. If so, it should be classified as a mitzvas aseh she’hazman gerama and not apply to women! (We actually discussed this one about a year ago as well, and my son spoke about it at his bar mitzvah, last year P’ VaYakhel-Pekudei.)
The Minchas Yitzchak brilliantly rescues the sevara for the hava amina by pointing to a suggestion in achronim that even though the building of the actual miskhan could not be done at night, the building of kelim could be done at night. If so, perhaps women could fulfill the mitzvah of binyan mikdash by building kelim at night, and one might have thought they could even do so on Yom Tov, kah mashma lan our pasuk that they may not. Based on this analysis it is also meduyak that the Mechilta offers an example of building the mizbeiach, a kli, and not building the walls of the mishkan itself.
I am still a bit puzzled. Unless I am mistaken, even Tosfos who holds women are not obligated in the aseh of Yom Tov still holds that one cannot be doche the lav of Y"T to fulfill a different aseh (yes, we discusssed this one as well in the past.) Doesn't that shoot down the hava amina here?