Having lived and studied in Crown Heights for several months--before which I believed that a significant proportion of Lubavitchers, perhaps 40% or half, did not believe the Rebbe was Moshiach--I have been surprised to find that the notion that the Rebbe is the presumptive, if not actual Messiah is very dominant in Chabad. Chabad Houses and conferences and other events "for the public" will not give this impression, as Chabad fears quite correctly that it will turn Jews off of Chabad, if not Judaism. But the fact is (or seems to be) that your average Chabad Anash in Crown Heights holds this belief.
Within this, there are varying degrees of subscription to the doctrine as well as vocality about it. While many, many take for granted that the Rebbe was the Nasi HaDor and the Moshiach HaDor, and almost as many would not hesitate to call him the "presumptive" Moshiach, only some are very convinced that he is/was the actual Moshiach, and fewer believe that he never physically died. The latter is, surprisingly, not a "fringe" belief in Chabad. It is a minority belief and not mainstream, but no one would be shocked to hear someone say it. That said, many of the people who subscribe to the belief that the Rebbe is Moshiach are quiet about it, especially among non-Chabad. And even within Lubavitch, there is something of a Don't Ask Don't Tell policy about this matter: although a large group of vocal Yechi elements do not include themselves in such a contract, many people who personally subscribe to the belief that the Rebbe is Moshiach--and especially those who don't--will not go out of their way to bring up the topic, whether with other Chabadniks or in public.
The questioner does not ask why the belief is so widespread. But, as someone who loves Chabad and the Lubavitcher Rebbe, I feel a bit of obligation to explain. (For more, please see Menachem Posner's answer to this questioner--I think it's very good.) The Rebbe was by any standard a great tzaddik. His genuine wisdom is immediately perceptible from his talks and writings. His words and actions motivated a worldwide movement to connect Jews with Torah, to assist Jews b'gashmius and b'ruchnius, and in many ways to unite am Yisrael. He indeed performed miracles, in the sense that miracles tend emerge from systematically positive action, speech, and thought. He was personally righteous, and there is no doubt that he brought about a new tradition for righteousness in the world.
Many Chabadniks who were zoche to meet the Lubavitcher Rebbe have family traditions of very meaningful encounters with the Rebbe, of good advice and miracles, and these stories--combined inevitably with cognitive biases, including that bias called love--sometimes produce the belief that the Rebbe is more than human. Whether or not this is correct is a separate matter. The Lubavitchers no longer have a living Rebbe; the Rebbe they did have was great and beloved; and these facts combined produce a yearning toward the past that is perhaps, after all, not totally out of place in Judaism.
So as much as the "official" policy where Chabad interacts with the world is to downplay this part of Chabad belief, when Chabad are safely within their own circles, it emerges with ardency and ardor. The curriculum in the in-town schools is very, very focused on the idea of "Moshiach," with or without explicit connection to the Rebbe. Discussions, blessings, and interactions between Chabadniks are similarly concentrated on "Moshiach" and the Ge'ulah. If one desires a statistical study, one has merely to count the number of "Yechi" kippot on the street in Crown Heights. (Lots; in 770 at least half. And these are the people who actively and vocally endorse the Rebbe as Moshiach.) In short, the idea that the Rebbe is Moshiach is not a secondary belief in Chabad. But it is perhaps worth asking whether this is belief is truly wicked, or simply the inevitable result of memory, grief, and longing.
I want to add, after further reflection, that it is the way of Chasidim not to believe things that it would be seriously grieving to believe. Some examples are the Holocaust and the Rebbe's histalkus and that Moshiach isn't here yet. I posit that self-deception, although not in fashion now, is actually a powerful psychological tool, and perhaps the only one by which one can survive.