Moshiach can come in the next 18 minutes--al pi halacha

Lubavitcher Rebbe, Igros Kodesh v.13, p.355 (Free Translation)

When speaking about matters connected to Moshiach, there are those who assert that this is, in the words of the gemora: הילכתא למשיחא [halachos which lack practical application in our day], but it should be known that this is not the case. The proof is found in the revealed part of Torah.

There is an opinion (Taanis 17a, Rambam Hilchos Bias Mikdash 1:7) which says that a Kohen is forbidden to drink wine even in our days because the Beis Hamidash will be rebuilt and one who is drunk is forbidden from performing the Avodah.

One can ameliorate the effects of alcohol in two ways: a) sleeping; b) the time it takes to walk a mil (Persian mile). Walking a mil takes 18 minutes [according to the widely accepted halachic opinion]. The most time it takes to walk a mil is 24 minutes [according to differing halachic opinion]. From here it is proven via the revealed Torah that within a short span of time, the time it takes to walk a mil, which is at most 23 minutes and 59 seconds—Moshiach can come with the Beis Hamikdash complete. And thus there would be a need [for the Kohen] to immediately be fit to perform the Avodah.