This is an interesting historic point. Most opinions would indeed maintain that Birkas Hamitzvos (as in Tefillin) is a rabbinic obligation- see Brachos 15a and Rambam Brachos 1:2. However there is a Tosefta (Brachos 7:1) which appears to derive the obligation of Birkas Hamitzvos from a pasuk regarding Birkas Hamazon which is a Torah obligation. Moreover the Yerushalmi has a hekesh (similarity derivation) from Torah to Mitzvos, that just as Torah requires a Bracha, Mitzvos require one too. Since the obligation to make a Bracha on Torah is from the Torah, this implies that Birkas Hamitzvos is from the Torah.

Rashi in the Torah also maintains this view as he brings regarding Maaser and the obligation to make a bracha on it (Devarim 26:13) which he derives from a pasuk. Thus we have a number of sources which maintain that Birkas Hamitzvos is already a Torah obligation and therefore Rabbeinu Tam's assertion that Michal made a Bracha could be based on these sources.

It is interesting to note that when Rashba (Teshuvos 1:123) brings Rabbeinu Tam's opinion regarding Michal he changes a few words, instead of saying that Michal would say a Bracha, he says regarding all women who put on Tefillin that they "seemingly should make a Bracha when placing the Tefillin." He seems to imply that Michal didn't make a Bracha but women following her lead can make a Bracha.

Yoel Domb