Rabbenu Tam states that it is a mitzvah me-doraita to count the days of the month, and even brings a pasuk. Why don't we make a brakhah for this counting as we do for sefirat ha'omer (to which this is compared by the braita)?
Rabeinu Tam explains his own words and says that the Mitzvah of counting the month refers to what is described in Megilah (5a). The Gemara there says that we do not take into account hours when calculating the length of a month (with regard to various matters). The Gemara there cites the verse which Rabeinu Tam here cites. RASHI there explains that the Gemara is referring to a Halachah mid'Oraisa (such as to know when a month has passed with regard to a Get that was given on condition that a month passes), and not to a Chiyuv d'Oraisa (such as to specifically get up and verbally count the months). Therefore, there is no Mitzvah here at all which would warrant the recitation of a Berachah.
Mordecai