The Rambam writes [הלכות מלכים ריש פי"א] that not only one who doesn't believe but also one who doesn't actively anticipate the coming of Moshiach is a kofer in Toras Moshe.
What I would like you to think about is - What is the Rambam's source that one must wait for Moshiach?? Why isn't it enough to believe?? And what is the LOGIC? To be a kofer means to harbor false BELEIFS so how does one who BELIEVES with all of his heart that Moshiach will come but doesn't wait for him become a kofer?? What compunds the problem is that the Rambam cites psukim there that don't prove his point!
Here is a shiur from Rav Moshe Schapiro ztz"l on the topic.