OPINIONS: The Gemara derives the Halachos of Shelishi for Terumah and Revi'i for Kodesh from either a Kal va'Chomer or from a Mah ha'Tzad. (See Chart.) These sources imply that the respective degrees of Tum'ah for Terumah and for Kodesh are mid'Oraisa. Are they indeed mid'Oraisa?
(a) RASHI here implies that the Halachos of Shelishi for Terumah and Revi'i for Kodesh are both mid'Oraisa, and that the Kal va'Chomer of the Gemara is a full-fledged Kal va'Chomer. Although each Kal va'Chomer which the Gemara suggests (to teach Shelishi and Revi'i) can be refuted by the argument of "Dayo," nevertheless the Gemara maintains that when a Kal va'Chomer will be rendered useless when the rule of "Dayo" is applied, "Dayo" is not applied and the Kal va'Chomer remains in effect.
(The problem of "Dayo" of the Kal va'Chomer that teaches Shelishi for Terumah is that the Chumra of a Sheni is that it itself is Tamei for Chulin, but not that it is Metamei other items. Hence, that law should not be able to teach, through a Kal va'Chomer, that a Sheni can make another item Pasul in the case of Terumah. The problem of "Dayo" of the Kal va'Chomer that teaches Revi'i for Kodesh is that one who is Mechusar Kipurim is only prohibited from eating Terumah, but he does not make Terumah that he touches Pasul, and therefore that law should not be able to teach, through a Kal va'Chomer, that a Shelishi makes Terumah become Pasul.)
This is also the opinion of TOSFOS in many places (Pesachim 19a, DH Lo; Chulin 35a, DH Ein Lecha; Chagigah 21b, DH Basraisa #2).
(b) However, RASHI in Chagigah (24a, end of DH Eino Din) and in Pesachim (19a, DH Amar Lei) asserts that the law of Revi'i for Kodesh is only mid'Rabanan. Rashi in Pesachim proves this from the fact that Rebbi Yosi -- who teaches the Kal va'Chomer -- maintains that a solid food is Mekabel Tum'ah from neither a liquid nor a solid food, but only from a Kli (vessel). Since a Kli can never be less than a Rishon l'Tum'ah, the food which touches the Kli becomes a Sheni, and the liquid which touches the food becomes a Shelishi, after which nothing else becomes Tamei, mid'Oraisa. Rebbi Yosi must be discussing the Tum'ah d'Rabanan of food or drink which touches another food, and thus the point of his Kal va'Chomer is to teach a Halachah d'Rabanan (i.e. the situation in which something can become Tamei with Revi'i l'Tum'ah).
Rashi cites further proof from the Gemara in Chagigah (21b) which states that the Chumra of Kodesh (that a Revi'i makes Kodesh become Pasul while only a Shelishi makes Terumah become Pasul) is only a "Ma'aleh d'Rabanan" which has no source in the Torah. (Tosfos in Pesachim cites a different Girsa of the Gemara in Chagigah. Tosfos also attempts to reconcile the Gemara in Chagigah with his opinion that Revi'i for Kodesh is mid'Oraisa, even according to Rashi's Girsa.)
(c) RASHI in Chulin (35a) seems to have a third opinion. Rashi explains that even the law of Shelishi for Terumah is only mid'Rabanan, and food that touches a Tevul Yom is also Pasul (as a Shelishi) only mid'Rabanan. According to Rashi, none of the Kal va'Chomers here are true Kal va'Chomers (perhaps because of the problem of "Dayo"), and they teach only Halachos mid'Rabanan.
This is also the opinion expressed by Rashi later in Chulin (128a, DH Mehader; see Gilyon ha'Shas and Rashash there), and it may also be the opinion of Rashi's second explanation in Chagigah (24a, DH Eino Din). (See Insights to Chagigah 24:1.)
Why does Rashi say that a Tevul Yom does not make Terumah become Pasul mid'Oraisa? The Gemara in Yevamos cites two sources from the Torah to teach that a Tevul Yom may not touch Terumah. One of the sources is the one Rashi cites here (beginning of 29b): the Torah clearly refers to a Kli which is a Tevul Yom and which remains Tamei until the evening with regard to Terumah. A Kli obviously cannot eat Terumah, and thus the verse must be teaching that a Kli may not touch Terumah.
How does Rashi in Chulin explain that verse? Apparently, Rashi learns that just as a person who is a Tevul Yom is prohibited from eating Terumah, a person or a Kli Tevul Yom is prohibited from touching Terumah. If, however, he does touch it, b'Di'eved the Terumah does not become Pasul. That is, the Gemara in Yevamos teaches only that a Tevul Yom is prohibited from touching Terumah, but not that the Terumah becomes Pasul (this is implicit in the words of Rashi in Yevamos).
The Acharonim cite a source for Rashi's opinion in Chulin from the Girsa of the Gemara of some Rishonim in Pesachim (35a; see Rabeinu Nisim Ga'on to Berachos 35b, and Tosfos to Menachos 21a, DH Yatzu), that after a person performs Tevilah when he is still a Tevul Yom he is actually Tahor, and the Torah merely made a special level of purity, a Ma'aleh, which prohibits him from eating Kodshim.
OPINIONS: Rebbi Yosi proves from a Kal va'Chomer that a Revi'i of Tum'ah will make Kodesh become Pasul. His Kal va'Chomer is from the Halachah of a person who is Mechusar Kipurim, who is "Pasul b'Kodesh" even though he is "Mutar b'Terumah." If a Mechusar Kipurim is Mutar b'Terumah but yet is Pasul b'Kodesh, then certainly a Shelishi -- which makes Terumah become Pasul -- should make Kodesh become a Revi'i (see Chart, footnote 7). When Rebbi Yosi refers to a Mechusar Kipurim's status with regard to Kodesh, he says that a Mechusar Kipurim is "Pasul" for Kodesh. Does Rebbi Yosi mean that a Mechusar Kipurim is merely prohibited from eating Kodesh, or does he mean that a Mechusar Kipurim is also able to make Kodesh Pasul by touching it?
(a) The RASHASH in Chagigah (beginning of 21a) asserts that a Mechusar Kipurim is not only prohibited mid'Oraisa from eating Kodesh, but he is even able to be Posel Kodesh, mid'Oraisa, by touching it. He proves this from the Gemara in Yevamos (74b) in which Rava infers from the verse (Vayikra 12:7) -- which teaches that the Mechusar Kipurim becomes Tahor after he brings his Korban -- that until that time the person remains Tamei. Rava concludes, therefore, that the Halachah that meat of Kodesh which touches something Tamei may not be eaten applies to meat of Kodesh which touches a Mechusar Kipurim before the person brings his Korban (see Rashi there, DH Kari).
(b) However, the wording of the Gemara here clearly implies that a Mechusar Kipurim is not Posel Kodshim mid'Oraisa, but that he is only Pasul from eating Kodshim mid'Oraisa. Although it is true that he is Posel Kodshim (Tevul Yom 2:4) -- that law is only mid'Rabanan. The RASHASH (Chagigah 24a) cites the Tosefta in Chagigah (3:7), which is the source for Rebbi Yosi's Kal va'Chomer, and the Yerushalmi in Chagigah (3:4), which both say that the Kal va'Chomer is from the Halachah that a Mechusar Kipurim is Posel Kodesh. Nevertheless, the Girsa of the Gemara here, the Gemara in Chagigah (24a), and the Gemara in Pesachim (18b) is that a Mechusar Kipurim is Pasul (not Posel) for Kodesh. This is also clear from the Gemara in Pesachim (35a, according to the Girsa of our text; see previous Insight) which teaches that a Mechusar Kipurim is Asur b'Kodshim mid'Oraisa only because of a Ma'aleh, but not because he is Tamei.
In fact, the TOSFOS HA'ROSH questions why the Gemara here says that a Mechusar Kipurim is only Pasul from eating Kodesh and is not Posel. Why should he not be Posel Kodesh as well because of the logic of the Rashash (that the Torah implies that he is Tamei and any Kodesh that a Tamei person touches becomes Pasul)?
The Tosfos ha'Rosh answers that the Torah does not actually refer to a Mechusar Kipurim as "Tamei." Rather, it says merely that after he brings his Korban, he "becomes Tahor." Only something explicitly called "Tamei" can be Posel items of Kodesh.
What, though, is the meaning of the Gemara in Yevamos which the Rashash cites as proof that a Mechusar Kipurim can be Posel Kodesh?
The Gemara there is expressing the opinion of Rava, who argues with Abaye about this point. Apparently, the Gemara here and the Gemara in Pesachim (35a) side with Abaye, who says that Kodesh touched by a Mechusar Kipurim does not become Pasul mid'Oraisa. (Rava will adopt the Girsa of the Rashash in the statement of Rebbi Yosi, that Mechusar Kipurim is Posel items of Kodesh.)