In the well-known sicha of Beis Nissan 5748 (Sefer HaSichos 5748, vol. 1, pgs 350, 351, 354), which marks 68 years since the Frierdiker Rebbe assumed leadership, the Rebbe discusses the concept of a Jewish king. The following are some of the main points of the sicha.
The relationship between the melech and the people is manifested in two opposite ways. On the one hand, the melech is totally exalted above the people which inspires awe and fear of the melech. On the other hand, the relationship between the nation and the melech is one of absolute connection. As the Rambam says, the melech is the heart of the Jewish people. We are the limbs. The connection that exists between the heart and the limbs of the body is the ultimate of closeness. Just like the body receives its life-force from the heart, the Jewish nation receives its life from the melech.
Not only does the nation receive its life from the melech, but the entire existence of the melech is dependent on the nation, as is written, "There is no melech without a nation." The fact that the nation is removed from the melech directly affects his malchus - for true malchus of a melech pertains only to those who are removed from him.
Therefore, the Rebbe continues, when the nation announces yechi hamelech, as was done in connection to Shlomo Hamelech and Dovid Hamelech, this affects not only the existence of the king, but the life of the melech as well.
The Rebbe further explains that every year on the day of Beis Nissan, the nation gets an increase in life through the leader of the generation, and the people of the generation increase the life of the Nasi through the declaration yechi hamelech. This is all the more so in the year of 5748, which marks 68 (gematria of chaim) years of the Frierdiker Rebbe's leadership.
Therefore, when the leader of our generation has attained the completion of chaim years of his service and deeds, there must be a fundamental increase of life by the act of the people through their declaration yechi hamelech -- for it expresses the fact that the time has arrived for "Arise and sing, those who dwell in the dust" -- my honored father-in-law, the Rebbe, Nasi of our generation -- and up to and including "Arise and sing," Dovid Malka Meshicha. In fact, these words (except for Dovid Malka Meshicha) were added by the Rebbe with his holy hand when editing the sicha for publication. This is the general content of the sicha. It is understood from the sicha that saying yechi hamelech brings about techiyas hamaisim.
The Rebbe also says that yechi hamelech brings the awakening of Melech HaMoshiach. It is interesting to note that we see a difference with the words that are used about the Frierdiker Rebbe. The Rebbe writes "Arise and sing, those who dwell in the dust", referring to the idea of techiyas hamaisim. In reference to Moshiach, the Rebbe did not add "Those who dwell in the dust." Only the words "Arise and sing" of Dovid Malka Meshicha are used.
The Rebbe also points out that Melech HaMoshiach has a greater connection to the nation than an ordinary melech since the neshama of every Jew has the level of yechida, which is a spark of Moshiach's neshama. Therefore, every Jew has the power to affect that which yechi hamelech accomplishes.