The Mordechai in Megillah Siman 798 has a case if a blind person can make kiddush for his family since (according to Rebbe Yehuda) a blind person is patur from mitzvas, then his obligation in making Kiddush is only m'drabbanan. Howe can the D'rabbanan be motzei (or help the others fufill) their obligation that is d'oraisa.
The Mordechai writes that we find a similar case in someone who makes Kiddush before it becomes night. That after plag hamincha (before the night but after a time someone can be makabel Shabbos) his obligation to make Kiddush would only be d'rabbanan (Tosesfes Shabbos is only d'rabbanan.) However when it becomes night there would be now a new obligation of kiddush m'doraisa. Still we say his kiddush made earlier takes care of the obligation that would be d'oraisa when it becomes night. This is the Mordechai's proof for the case of a blind person.
The Minchas Chinnuch brings this in regards to the question of how a Katan that becomes a bar mitzvah during sefira could continue counting with a bracha, his chiyuv before was only m'drabbanan and now is d'oraisa. However we see from the cases of the Mordechai that this question is answered.
However there is a question that one could ask on the Mordechai. The Gemorah in Brachos (Daf 20) says that a Katan who ate and now has to say bircas hamazon (m'drabbanan) cannot be motzei a Gadol that also ate a seudaha and is full that has to say bircas hamazon d'oraisa. Seemingly this is a kasha (question/difficulty) on the psak of the Mordechai. What achronim speak about this? What answers are given?
Yehoshua, Yerushalayim, Eretz Yisrael
1. This question is asked by the Magen Avraham (OC 267:1): a Katan cannot be Motzi a Gadol even though the Katan later will reach adulthood and have a Torah obligation, so how can one be Yotzei Kidush mid'Oraisa before it is Shabbos mid'Oraisa simply because later on when it becomes dark one will attain a Chiyuv d'Oraisa?
2. An answer to this question is given by the Maharam Shik (Mitzvah 307:3, cited in note 14 to Minchas Chinuch #306 in the Machon Yerushalayim edition). The Maharam Shik answers that there is a distinction between a Katan and a blind person, or an adult before Shabbos has commenced mid'Oraisa. A Katan possesses no Mitzvah whatsoever to say Birkas ha'Mazon, but rather his father has a Mitzvah to educate him to say Birkas ha'Mazon. In contrast, in the case of a blind person -- even though he is exempt from the Torah prohibition according to Rebbi Yehuda -- Rebbi Yehuda agrees that mid'Rabanan that he is obligated in all the Mitzvos. Since he is obligated mid'Rabanan for the Mitzvah, this automatically means that he is also obligated mid'Oraisa since the Torah states, "You shall not depart to the right or to the left from the words which the sages will tell you" (Devarim 17:11), from which we learn that every Mitzvah of the Rabanan is also a Torah Mitzvah. (This is the opinion of the Ramban -- that every Mitzvah d'Rabanan is automatically a Mitzva d'Oraisa, and the only difference between a d'Oraisa and a d'Rabanan is that in cases of doubt we say Safek d'Oraisa l'Chumra, while we say Safek d'Rabanan l'Kula.)
3. However, the Minchas Chinuch does compare the Katan to the blind person. The Minchas Chinuch is consistent with his opinion that a Katan also has a Mitzvah to say Birkas ha'Mazon and it is not merely a Mitzvah incumbent on his father to educate him. This is stated by the Minchas Chinuch in Mitzvah 17:14 (DH u'Mevu'ar), that in reality a Katan is a "Ben Mitzvos." It is not possible to say that the Torah warned him, because the Katan does not possess "Da'as," intelligence. However, writes the Minchas Chinuch, the minor is obligated in Mitzvos.
Here is another answer to your question, also given by the aforementioned Maharam Shik:
1. The concept of "Arvus," that "Kol Yisrael Arevim Zeh l'Zeh" -- all of Klal Yisrael are responsible for each other, is derived by the Gemara in Shevuos 39a from the verse, "And they shall stumble each upon his brother" (Vayikra 26:37). We also learn from this that since every Jew is responsible for every other Jew, one person may recite a blessing and be "Motzi" his fellow Jew with his obligation.
2. The question now arises whether this concept of Arvus applies also for Mitzvos d'Rabanan. The Maharam Shik proves that it does, also from the Gemara in Shevuos 39a which states that before Bnei Yisrael entered Eretz Yisrael they accepted upon themselves this Arvus responsibility. The Gemara there says that they even accepted responsiblity for Mitzvos which would be introduced only later, such as the reading of the Megilah on Purim. (See also Pri Megadim, Mishbetzos Zahav OC 167:17.)
3. Now, if Arvus applies also for Mitzvos d'Rabanan, it follows that even if the blind person is liable only mid'Rabanan in Mitzvos, nevertheless the principle of Arvus applies for him and consequently he can exempt members of his family who are obligated mid'Oraisa.
4. In contrast, for the Katan the concept of Arvus will not work because (as the Mordechai maintains) a minor is not obligated in Mitzvos at all, even mid'Rabanan, but rather the Mitzvah rests solely upon his father to educate the minor. (This is the simple way of looking at this matter, not like the Chidush of the Minchas Chinuch that I cited in my first reply.)
5. This, therefore, is the distinction between the blind person and the minor. Since the blind person is obligated mid'Rabanan in Mitzvos, it follows that Arvus applies for him and he can be Motzi people who are liable mid'Oraisa. In contrast, the minor is not obligated in Mitzvos at all, not even in Mitzvos d'Rabanan, but rather his father has an obligation to educate him. Therefore, the Gemara in Berachos says that a Katan cannot be Motzi a Gadol in Birkas ha'Mazon.
Shouldn't there be a Chiluk whether I want to rely on his Ma'aseh or his Dibur?
-1- If a Katan is obligated to perform an act MiDerabanan then perhaps I, (being Mechuyav MiDeraissa), cannot rely on him.
Such would be the case where the Katan is blowing a Shofar .
-2- However where I am answering to the Bracha of a Katan, or answering to someone who is saying Kiddush MiDerabanan,
then the Din of Shome'ah K'Oneh should accomplish that it is as if I said these words.
And although my Chiyuv is Deraissa, I should be Yotze.
The Gemara in Berachos (20b) relates that Ravina asked Rava if women are obligated mid'Oraisa to recite Birkas ha'Mazon, or only mid'Rabanan. Ravina explained that if they are obligated mid'Oraisa, then they may be Motzi other people (men) who are obligated mid'Oraisa, while if they are obligated only mid'Rabanan, then the principle of "Kol she'Einu Mechuyav b'Davar Eino Motzi Es ha'Rabim Yedei Chovasan" applies -- someone who is not obligated in a Mitzvah (d'Oraisa) cannot be Motzi others.
We learn from this Gemara that there is no distinction between a Ma'aseh and a Dibur. Even if a Mitzvah depends only on speaking, if the Berachah is said by someone who is only obligated mid'Rabanan, then someone who is obligated mid'Oraisa cannot answer and thereby fulfill his Mitzvah.
Isn't there an additional issue? For someone to be motze someone else he should have at least the same level of obligation whether he himself was already yotze or not. Women should not be motze men for shofar blowing because for them it is a mitzvah shehazman grama so they are only yotze voluntarily. If the blind man is not really mechuyav D'Oraysa I don't see how the Mordechai's and the Maharam Shik's positions obviate this issue.
1. The answer of the Maharam Shik is based upon a big chidush that every Mitzvah d'Rabanan is really a Mitzvah d'Oraisa. The Torah says in Parshas Shoftim (Devarim 17:11), "You shall do according to the Torah that they (the Kohanim, Leviyim, and judges in the Beis ha'Mikdash) shall instruct you.... You shall not depart right or left from what they tell you."
2. We learn from this verse the Mitzvah d'Oraisa to listen to Chazal. The only difference between a Mitzvah d'Oraisa and a Mitzvah d'Rabanan is where there is a doubt. In the case of a doubt about a Mitzvah b'Oraisa, the rule is Safek d'Oraisa l'Chumra and one must be stringent. In contrast, in the case of a doubt about a Mitzvah d'Rabanan, the rule is that one conducts himself leniently, because this was the condition that Chazal made when they instituted their enactment -- that in cases of doubt one may be lenient. (See sources for this in the Rambam's Sefer ha'Mitzvos in Shoresh Rishon, Ramban there #4, and Minchas Chinuch 495:3.)
3. Therefore, even according to Rebbi Yehudah (Bava Kama 87a) who says that a blind person is exempt from Mitzvos, nevertheless since he is obligated mid'Rabanan it follows that in effect he is obligated mid'Oraisa. As such he may be Motzi his family according to the Mordechai.
4. In contrast, a woman is not obligated even mid'Rabanan to blow the Shofar on a compulsory basis, so she cannot be Motzi a man.