- Mashiach will come today
- Mashiach can come today
- Mashiach cannot come on all days but he will come
The second view is what I have seen elsewhere in the name of the Brisker Rav. It means that every morning we have to wake up and think that today might be the day that Mashiach comes. Indeed, it seems to be the simple meaning of the paraphrase of Rambam's 12th fundamental principle in the "Ani Ma'amin" (printed in most prayerbooks): "And though he may delay, I wait daily for his coming" (translation from the Koren Sacks Siddur, p. 204). "Wait daily for his coming" seems to mean that he can come on any day.
II. Not Every Day
The third view is that of R. Yehuda Henkin (ibid., also in the name of his illustrious grandfather, R. Yosef Eliyahu Henkin; see this post: link). R. Henkin marshal impressive sources to make his point. For example, the Gemara (Eruvin 43a-b) discusses someone who vows to be a nazir beginning on the day that Mashiach comes. Must he refrain from the activities prohibited to a nazir (e.g. drinking wine) immediately, in case Mashiach comes today? The Gemara rules that he may drink on Shabbos and holidays but not during the week -- because Eliyahu, who will precede Mashiach, will not disrupt our preparations for Shabbos and holidays by coming on the prior day. It seems clear from this Gemara that there are some days -- namely Shabbos and holidays -- on which Mashiach cannot come.
Similarly, the Gemara (Rosh Hashanah 10b-11a) contains a debate between R. Eliezer and R. Yehoshua over whether the ultimate redemption will happen in the month of Tishrei or the month of Nissan. Clearly, according to either sage, there are 11 months in the year during which Mashiach will not come. And there are other similar passages in the Talmud that limit the days on which Mashiach can come. This all seems to prove R. Henkin's point.
III. Defending the Any Day View
I recently saw a defense of the second view by R. Moshe Mordechai Shulzinger in various places in his Mishmar Ha-Levi (collected in the book Ma'ayanos Ha-Emunah [Bnei Brak, 3rd ed. 2007], pp. 517-535). R. Shulzinger points to an explanation of the Gemara in Eruvin that explains how the Brisker Rav must have understood the texts cited by R. Henkin. R. Yonasan Eybeshutz, in his commentary to Shulchan Arukh, Yoreh De'ah (Kereisi U-Fleisi, end of ch. 108), explains that there are two ways for Mashiach to come -- 1) at the appointed time, 2) at an earlier time if we deserve it. In the latter scenario, Mashiach can come immediately, without prior announcement by Eliyahu. However, this is an extremely unlikely occurrence, as opposed to the former way, which is an historical eventuality. Therefore, regarding a nazir, the Gemara is only concerned with the historically certain event of Eliyahu coming and then Mashiach, and not the remote possibility of an immediate messianic appearance.
This can also explain all of the other Talmudic passages. The appointed time is a subject of debate -- it might be in Tishrei or in Nissan. There are certain days -- such as Shabbos and holidays -- that cannot be the appointed time. However, the unannounced time, when we deserve and immediate redemption, can happen on any day. Therefore, says R. Shulzinger in explanation of the Brisker Rav's view, we are obligated to believe that maybe we will somehow, based on a calculus that we might not understand, deserve Mashiach today. Or maybe it is the appointed time. Either way, somehow there is a possibility that today is the day.