The Gemara in Zevachim (beginning of 33b) states in the name of Rebbi Avahu that the verse of "b'Chol Kodesh Lo Tiga" refers only to a Tamei person who touched Kodesh. Rashi (DH l'Tamei) writes that Reish Lakish (cited in Zevachim 32b) derives Malkus from this verse only for a Tamei person who touched Kodesh, while this verse is not referring to one who enters the Beis ha'Mikdash at all.

Therefore, one cannot derive the Azharah for ha'Ba l'Mikdash Tamei from "v'El ha'Mikdash Lo Tavo" because this verse has nothing to do with entering the Mikdash, according to the conclusion of the Gemara in Zevachim. (Even though, at the beginning of the Sugya in Zevachim, Resh Lakish did learn from this verse that even if the Tamei person merely put his hand into the Beis ha'Mikdash he receives Malkus, later he retracted from this position.)

Kol Tuv,

Dovid Bloom

Here is another answer, given by the Si'ach Yitzchak (Makos 14b, DH Lachen):

1. The Si'ach Yitzchak comments on the Mishnah (13a) that the Tana attempted to list examples of prohibitions which are not only liable for lashes but are also Isurei Kares. This list includes a Tamei person who ate Kodesh or who entered the Beis ha'Mikdash. The Chidush of the Mishnah is that although the transgresser is punished with Kares, he also receives Malkus.

2. The Si'ach Yitzchak writes that it is very surprising why the Lav of "El ha'Mikdash Lo Tavo" (Vayikra 12:4) is not mentioned by the Gemara. This would have been much more appropriate than "And they shall not make their camps Tamei," because the latter prohibition refers to all types of camps (for example, a Metzora entering the camp of Yisrael, or a Zav entering the camp of the Leviyim), while the Mishnah refers specifically to a Tamei person entering the Beis ha'Mikdash itself.

3. The Si'ach Yitzchak answers his question on the basis of his earlier words (cited above in #1). Rashi (Vayikra 12:4) writes that a woman who has just given birth is considered a "Tevulas Yom Aruch" -- she has gone already to the Mikvah but she must wait for a "long day" (33 or 66 days, depending on whether she had a boy or a girl) until she is permitted to enter the Beis ha'Mikdash. One learns from the Rambam (Hilchos Bi'as ha'Mikdash 3:9) that a Tevul Yom who enters the Beis ha'Mikdash is not liable for Kares. This is why the Gemara does not mention the Lav of "El ha'Mikdash Lo Tavo"; the Gemara wants to enumerate prohibitions which also include Kares.

4. However, the Mesivta edition of the Gemara cites the Or Same'ach (end of Hilchos Pesulei ha'Mukdashin 18:14, based on Rambam, Hilchos Bi'as ha'Mikdash 3:14) who disagrees with the Kesef Mishneh and maintains that according to the Rambam, a Tevul Yom is Chayav Kares for entering the Beis ha'Mikdash. According to this, we still have no answer for why the Gemara did not cite the verse of "El ha'Mikdash Lo Tavo."

Kol Tuv,

Dovid Bloom