While the halacha that a kiddush Hashem b'rabim must take place in the presence of an "edah" is derived from a possuk in Emor (Vayikra 22:32), the definition of the term "edah" is established by the Gemara (Megillah 23B) based on a possuk in this week's parsha (Bamidbar 14:27). Of the twelve meraglim, only Yehoshua and Kalev conveyed a proper report while the other ten sinned and delivered a terrible report. When complaining about the ten sinners, Hakodosh Boruch Hu refers to them as an "edah ha'ra'ah", and we thereby understand the halacha that kiddush Hashem b'rabim must be in the presence of ten Jews. This passage in the Gemara seems so strange - we establish the concept of a minyan based on the fact that there were ten evil meraglim!
Perhaps what the chachomim had in mind with this derivation was the following: The Rambam writes[1] that we have halochos that are based on the premise that only the Jewish people who live in Eretz Yisroel constitute Klal Yisroel; all of the millions of Jews who live in chutz la'aretz are considered to be yichidim - individuals (Ta'anis 14B.) (Those who live in chutz la'aretz but view Eretz Yisroel as their national homeland are also considered, to a lesser degree, part of Klal Yisroel.) The din of kiddush Hashem b'rabim really should have required the presence of all of Klal Yisroel, but, as we said above, we derive from this week's parsha that wherever there is a minyan of Jews they represent Klal Yisroel[2] and the Shechinah is present there. Perhaps the chachomim could only derive this principle from the meraglim since after yetzias Mitzrayim they were the only Jews who had stepped foot in Eretz Yisroel.
[1] In his commentary to Mishnayos B'choros (29) and in Sefer Hamitzvos, Mitzvos Aseh 153
[2] Rabbi Yosef Dov Soloveitchik, Divrei Hogus V'ha'aracha, pp.114 - 116.