In defense of Jewish outreach to xians, the following idea from the Aleinu prayer which is said at the conclusion of all three daily prayer services was brought...
"...so that all of living flesh will call on Your Name...."
Let's look at the whole thing.
"We must praise the Master of all, and render greatness to the Creator of the universe, Who did not make us like the nations of the lands, and did not place us like the families of the earth, Who did not make our lot like theirs, or our destiny like all of them, For they bow down to nothingness and emptiness, and pray to a god that will not save, But we bow down low in grateful acknowledgement before the King over the kings of kings, The Holy One, blessed be He. For He spreads out the heavens and establishes the earth, and His majestic abode is in the sky above, And His mighty dwelling place in the lofty heights. He is our God; there is none else. He is truly our King; none is like Him. As it is written in His Torah, "Know this day and reflect on it, because the Eternal is our God in the sky above and the earth below. There is none else." (Deut. 4:39)"
"Eternal our God, we therefore hope soon to see Your majestic glory; To remove idols from the earth, so that the false gods will be destroyed; To perfect the world under the Almighty's kingdom, so that all will call on Your name; To turn all the wicked of the earth toward You so that all the inhabitants of the world will realize and know that to You every knee must bow down, every tongue swear allegiance. Eternal our God, before You they will bow down and fall, and honor Your glorious name. And they will all accept the yoke of Your kingdom, that You might rule over them soon and forever, for the kingdom is Yours, and to the ends of eternity You will rule in glory. As it is written in Your Torah, "The Eternal will rule forever." (Exodus 15:18) And it has been said, "The Eternal will become King over the entire earth. On that day, the Eternal shall be One and His Name shall be One." (Zechariah 14:9)"The Aleinu prayer first presents a realistic view of our current reality and then proceeds to beautifully express the hope for the vision of messianic times when the whole world will abandon false ways and acknowledge G-d's sovereignty over the whole world.
But it is itself not without controversy. See Aleinu: A popular prayer with a controversial history.
Rabbi Mendel Kessin has explained that we help bring the redemptive vision closer through our performance of mitzvot, our teshuvah and our suffering. I don't see how missionizing the goyim to the Sheva Mitzvot Bnei Noach accomplishes our mission. It's up to them to search out the truth which has been made available for themselves. And those who have been so moved by their desire to know the truth will surely find it, even without our intervention. Their own law says that they are to set up courts of justice. We weren't told to do it on their behalf. They must do it for themselves. Just something more to think about.