Short answer: the Lord will bring all of His chosen ones to Himself which consist of Jews and Gentiles (for there is no distinction), but He will bring a great many ethnic Jews to faith by the end.
First of all, I want to make it clear that I will be answering this question from a Covenantal perspective on Scripture which effects both my eschatology and my hermeneutical mindset; I don't want that to be hidden.
I think one of the clearest passages on this particular issue is, in its entirety, Romans 9 through Romans 11. Romans 9 begins in the NASB with
I am telling the truth in Christ, I am not lying, my conscience testifies with me in the Holy Spirit, that I have great sorrow and unceasing grief in my heart. For I could wish that I myself were accursed, separated from Christ for the sake of my brethren, my kinsmen according to the flesh, who are Israelites, to whom belongs the adoption as sons, and the glory and the covenants and the giving of the Law and the temple service and the promises, whose are the fathers, and from whom is the Christ according to the flesh.
Here Paul clearly establishes that he is speaking about physical descendants of Abraham, that they are not currently believing in Christ (so they will perish), and that adoption as sons still belongs to them as an ethnic people. Paul continues in verse 6
But it is not as though the word of God has failed. For they are not all Israel who are descended from Israel; nor are they all children because they are Abraham’s descendants, but: “through Isaac your descendants will be named.” That is, it is not the children of the flesh who are children of God, but the children of the promise are regarded as descendants.
Here Paul tells us that not everyone who is descended from Jacob is one of God's children in the same way that Ishmael, the child of Abraham, was not regarded as a child of the Promise. We see this clearly happening with those who fell away in Israel, even with entire tribes like Dan. So not everyone who we humans would consider to be Israelites are Israelites.
The Covenantal perspective would take this a step further and say that we Gentiles have been grafted into Israel and have become Israelites ourselves according to God's sovereign choice.
For the sake of brevity, I'll skip Romans 10, though it still is important to read; in Romans 11:1 (text below) we see Paul say that "God has not rejected His people, but that Paul, himself, is evidence of God's faithfulness to the people, though he is nearly alone in the same way that Elijah was alone. God's response to Elijah was that He would preserve a perfectly large number of Jews for Himself (7000 being 7x1,000 where 7 is the number of perfection, and 1000 stands for an undefined great number) and Paul tells us that this situation applies to him as well, aka a great many ethnic Jews will come to faith.
I say then, God has not rejected His people, has He? May it never be! For I too am an Israelite, a descendant of Abraham, of the tribe of Benjamin. God has not rejected His people whom He foreknew. Or do you not know what the Scripture says in the passage about Elijah, how he pleads with God against Israel? “Lord, they have killed Your prophets, they have torn down Your altars, and I alone am left, and they are seeking my life.” But what is the divine response to him? “I have kept for Myself seven thousand men who have not bowed the knee to Baal.” In the same way then, there has also come to be at the present time a remnant according to God’s gracious choice.
Lastly, I'll point you to Isaiah 19 which speaks about how the Lord will bring pestilence to Egypt, which will result in their repentance and their turning to the Lord. It tells us in verse 19 that "In that day there will be an altar to the Lord in the midst of the land of Egypt, and a pillar to the Lord near its border," which tells us that all throughout Egypt the Egyptians will be praising the Lord (an event which hasn't happened). Later in verse 23, we are told
In that day there will be a highway from Egypt to Assyria, and the Assyrians will come into Egypt and the Egyptians into Assyria, and the Egyptians will worship with the Assyrians. In that day Israel will be the third party with Egypt and Assyria, a blessing in the midst of the earth, whom the Lord of hosts has blessed, saying, “Blessed is Egypt My people, and Assyria the work of My hands, and Israel My inheritance.”
So we see that Israel, through Judah, will once again become a nation that worships and serves the Lord. What a marvelous future for the Gospel there yet remains!