Gemara

(Mishnah - R. Chanina Segan ha'Kohanim): Kohanim would burn [Kodesh] meat that was not a Rishon l'Tum'ah with meat that was a Rishon, even though this increases the Tum'ah of the former.

(Rav Yehudah): The former meat was a Shelishi.

Question: Food is not Metamei food!

Answer: There are liquids with the meat. The liquids are Metamei the Shelishi.

115b (Rav Chisda): [Even though] one washed his hands for the first dipping [at the Seder], he must wash for the second dipping.

Sukah 26b (Mishnah): Once, they brought to R. Tzadok less than k'Beitzah to eat. He wrapped it in a cloth and ate it outside the Sukah, and did not bless afterwards.

27a - Inference: Had it been k'Beitzah, he would have needed to eat it in the Sukah.

Rejection: No. A k'Beitzah would have obligated Netilas Yadayim and a Berachah Acharonah.

Eruvin 21b (Beraisa): Once, R. Akiva was imprisoned. He used to get a [meager] ration of water. One day, he received only half. Even though he was in danger due to lack of water, he used [much of] it to wash before eating.'

Rishonim

Roke'ach (328): If one eats less than a k'Beitzah [of bread], he washes due to Safek, and does not bless.

Beis Yosef (OC 158 DH Kasav): It seems that since less than k'Beitzah is not Mekabel Tum'as Ochlim, perhaps Chachamim did not obligate Netilas Yadayim. Or, perhaps they obligated Stam, even less than k'Beitzah.

Roke'ach (283): One blesses when washing [before eating the Matzah] because he must immerse the Maror. He need not wash for eating Matzah, since one is Yotzei with a k'Zayis. One need not wash for less than a k'Beitzah, like it says in Sukah and Berachos. Therefore, he washes for the Maror.

Note: Beis Yosef (ibid.) cites the Roke'ach to say 'one need not wash for less than a k'Zayis.'

Hagahos in Shulchan Aruch ha'Shalem (OC 158:17): Also the Magen Avraham cites the Roke'ach to say 'like it says in Sukah and Berachos.' We do not find this in Berachos. Birkas Eliyahu (on Bi'ur ha'Gra) says that it refers to Berachos 48a. Perhaps he means 45a, which says that we bless Birkas ha'Mazon for a k'Zayis. If so one must also wash for a k'Zayis. The Gra connects Birkas ha'Mazon and washing. Berachos 53b brings an Asmachta for Netilas Yadayim and Birkas ha'Mazon from the same verse ("v'Hiskadishtem...") Damesek Eliezer says that the text should say "Sukah and Chulin." Chulin 107a brings the episode with R. Tzadok.

Tosfos (Pesachim 14a DH d'Ika): The Riva learns from here that less than a Revi'is of liquids is Metamei. Presumably, there is less than a Revi'is of liquid on the meat. Also below (17b) we say that less than a Revi'is of water is Tamei. In Avodah Zarah 31b we say that a Revi'is is Tamei. This refers to being Metamei [mid'Rabanan] one who drinks Tamei liquids. The Ri says that when the Tum'ah is not mid'Oraisa, e.g. Stam wine of Nochrim, we require a Revi'is. R. Tam says that mid'Oraisa a Revi'is is Metamei others, and mid'Rabanan any amount is.

Tosfos (115b DH Tzarich): Rav Chisda does not literally mean that one must wash for the second dipping. It is after ha'Motzi. One washed for the Matzah! Rather, the washing for the Matzah is also for the second dipping.

Poskim

Shulchan Aruch (OC 158:3): Some say that one need not wash for less than k'Zayis.

Taz (3): It is explicit in Sukah (27a) that one need not wash for less than a k'Zayis.

Mishbetzos Zahav: Also the Levush exempts for less than k'Zayis, for it is not an important Shi'ur for all Isurim. I explain the Beis Yosef's text as follows. We bless only for [washing for] the second dipping, but we would not bless for a k'Zayis of Matzah. It is not astounding not to bless on less than a k'Beitzah, for it is clear from Sukah that one need not wash for less than a k'Zayis. One may eat Arai outside a Sukah. Less than k'Zayis is surely Arai. Likewise, the enactment of Netilas Yadayim was only for one who fixed to eat, but not for Arai. In my introduction [to Orach Chayim] I wrote that according to the opinion that Terumah of Peros is mid'Oraisa, we require Netilas Yadayim only for bread [of Chulin] because it is Keva [fixed]. Pas ha'Ba b'Kisnin (cake) is Arai, like Peros. It says so in Bedek ha'Bayis in Toras ha'Bayis ha'Aruch (6:1). The Roke'ach teaches two matters, that we do not bless on [washing for] a k'Zayis, and that we need not wash at all for less than a k'Zayis. This is somewhat difficult, but it explains the Beis Yosef and Taz.

Magen Avraham (4): The Beis Yosef's text of the Roke'ach is mistaken. It should say 'less than k'Beitzah', for one must eat a k'Zayis! This entire Sa'if is a mistake. Also Divrei Chamudos (Chulin 8:72) says so.

Eshel Avraham: The Magen Avraham explains that the Roke'ach answers Tosfos' question. (Why did Rav Chisda say that we wash for the Maror? In any case we must wash for the Matzah!) If so, in Siman 328, where the Roke'ach said that for less than k'Beitzah we wash without a Berachah, the same applies to less than k'Zayis. This is like Rashi said, that it is merely for cleanliness. If so, there is a slight contradiction in the Roke'ach! I answer that in Siman 283 he teaches that less than k'Beitzah does not need specifically Netilas Yadayim. A cloth suffices. This is like Tosfos (Yoma 79b DH Ha), that for Chulin [bread] even a Kohen may not rely on a cloth. Chachamim were not stringent for less than k'Beitzah, but k'Beitzah requires washing with water. A cloth does not suffice. Since a cloth suffices for less than k'Beitzah, we cannot bless Al Netilas Yadayim. We similarly hold that one who urinates before Tefilah does not bless Al Netilas Yadayim, since it suffices to clean his hands in earth. However, if so, why does one bless for Terumah, and how did they enact a Berachah for Chulin?

Machatzis ha'Shekel: The Roke'ach holds like Rashi (Pesachim 115a DH Tzarich), that one blesses for washing for foods dipped in liquids.

Gra (DH Im): The Magen Avraham proves from Pesachim that the text of the Roke'ach must say 'less than k'Beitzah.' It says that one must wash for the Maror. Mid'Oraisa, any amount of anything dipped is Mekabel Tum'ah due to the liquid (Tosfos 14a). However, Tosfos says that the washing is also for the Matzah. This does not prove that he holds that one must wash for less than k'Beitzah. Tosfos did not want to say that the Gemara assumes that one will not eat a k'Beitzah of Matzah in the entire meal. Really, the primary opinion obligates washing for a k'Zayis. Any amount is Mekabel Tum'ah, but Chachamim decreed only on what requires Birkas ha'Mazon. This is why in Sukah we connect Berachah and washing. In Berachos 53b, there is an Asmachta for both of them from one verse. Also, if it were due to Tum'ah, one could break bread into small pieces, each less than k'Beitzah, to avoid the need to wash. If so, why did R. Akiva need to pain himself and deprive himself of water? He could have broken the bread into small pieces! The same applies to one who travels [and will not have water. Why were Chachamim lenient to let him wash once in the morning for the entire day (Chulin 107a)?]

Damesek Eliezer: The Roke'ach holds that even though one need not wash for less than k'Beitzah of bread, one must wash for less than k'Beitzah of a dipped food if it is still wet, like Tosfos (14a), who says that it is Metamei. Even according to R. Chananel, who requires a Revi'is of liquid to be Metamei others, one must wash for any amount of liquid, lest it be Metamei his hands. The Magen Avraham (Sa'if Katan 3) said that Tosfos disagrees with the Roke'ach. I.e. Tosfos 115b holds that the Gemara could have said that the second washing is for the Matzah. The Gra explains that if we exempt from washing for less than k'Beitzah because it is not Metamei others or is it not Mekabel Tum'ah mid'Oraisa, the same should apply to much bread, if each piece is less than k'Beitzah. Rather, it depends on Birkas ha'Mazon. R. Tzadok holds that only k'Beitzah obligates Birkas ha'Mazon.

Mishnah Berurah (10): The Taz, Bach, Gra and Birkei Yosef in the name of Rashbatz exempt from washing for less than k'Zayis. Divrei Chamudos, the Magen Avraham, Eliyahu Rabah and others say that it is like less than a k'Beitzah. He washes without a Berachah. L'Chatchilah, one should be stringent. All agree that one must wash for a k'Zayis, even if it is comprised of tiny crumbs. One blesses for k'Beitzah of crumbs. If one eats a little bread to counter the sharpness of a drink, so the bread is secondary and he need not bless ha'Motzi, he need not wash, even for k'Beitzah of bread. Some disagree. Surely one may be lenient for less than k'Zayis, since some always exempt this. One should be stringent for a k'Zayis or k'Beitzah.

Kaf ha'Chayim (10): The Beis Meir says that the custom is not to wash for less than k'Zayis. It is proper to wash to fulfill all opinions. In any case, some are careful not to eat less than k'Zayis, for then one cannot bless afterwards. This applies to bread more than to other foods.