Some gematrias of 68:
(see בעל הטורים on ויקרא כג:מ) lulav.....לולב
(see here) שם בן מ"ב] הויה]
(see here) all life..... כל חי
The most famous of these gematrias is חיים, and in fact, it's common practice that when something has a value of 68, rabbis will write that it's כמנין חיים (like the gematria of "Hayim"). In fact, each of the links mentioned above includes that phrase.
The State of Israel is 68 years old. Although there are many views pertaining to the religious significance of the State of Israel, it seems to me that the state is a blossoming of the shell that protects the fruit inside it. It is a necessary protection for both the holy Land of Israel and the holy Jewish people that dwell inside it. When the shell eventually opens up, we will be able to enjoy the fruit of Mashiah ben David. Until then, we have the shell of the State of Israel, albeit imperfect, having the aspect of Mashiah ben Yosef.
And we must be thankful for it since prior to the blossoming of the shell, the tree was bare. Fruits kept on popping up directly from the tree, but they had no shell to protect it from the elements. Mashiah ben Yosef is supposed to prepare the world for the coming of Mashiah ben David. That is what the State of Israel is doing. It is by no means perfect, and in some cases, it has actually caused the spiritual downfall of some Jews. However, it is by-and-large a positive development in history that has caused the flourishing of Torah and Torah education by huge groups of Jewish people.
Nevertheless, we know that we are still not out of Galut and huge steps must occur to make that happen. That is not to say that the Geula is far away. Not at all. In fact, one can hint that the 68 years, which are כמנין חיים, are a hint to what comes next.
The gemara in Sukkah 52a seems to imply that this verse is referring to Mashiah ben David in response to what occurs to Mashiah ben Yosef and is asking for his own life. Others like the Gr"a and the Ariza"l apply the verse to Mashiah ben Yosef himself. The old Mashiach Awareness blog explains how to explain the gemara according to that view.חַיִּים, שָׁאַל מִמְּךָ--נָתַתָּה לּוֹ; אֹרֶךְ יָמִים, עוֹלָם וָעֶדHe asked life of Thee, Thou gavest it him; even length of days for ever and ever.
According to the view of the Gr"a and Ariza"l, it's possible that Mashiah ben David asked that the State of Israel be given חיים years, which was granted by HKB"H, after which time, (according to the second part of the verse,) the shell of the fruit will open up and the ripe fruit of Mashiah ben David will spread throughout the world forever (ארך ימים עולם ועד).
May this occurrence take place very soon, Amen.