Just like among the Modern Orthodox in the United States, where some elements are trying to connect it to Chassidism, similarly, in the land of Israel, there are some who are trying to bring the Dati Leumi and Chassidus closer together. However, just as in the USA, there are others in the camp opposing and resisting such a major shift as well.
In Israel, this recently came into public view in a major way, the trigger being a debate about if it was appropriate for Dati Leumi people to join in celebrations of the Yud Tes Kislev holiday of Lubavitcher Chassidim. A popular Dati Leumi website ran two articles by הרב ברוך אפרתי related to the subject, one opposing the celebration of Yud Tes Kislev, and the other citing Rav Tzvi Yehudah Kook, the great Dati Leumi Torah leader, as saying that the Vilna Gaon was their Rebbe, among other things.
Baruch Hashem there are people there that are standing up for their longstanding traditions. May we be zoche to a peaceful resolution of this matter soon.