Two of the remaining covenants are definitely dealing with Israel as a whole: the Abrahamic covenant and the Mosaic Covenant. I think that we can add the New Covenant in to that as well, although for that one we are dealing with "spiritual Israel" and not "national Israel". The main figures of these covenants all share in an aspect of intercession. The most obvious being Christ interceding for His people at the throne of God. But for this post, I want to look at the intercessions of Abraham and Moses.
In the case of Abraham, God establishes His covenant with Abraham in Genesis 15. Then, in Genesis 17 it's reaffirmed with circumcision given as the sign. Immediately after, in chapter 18, we read:
The Lord said, “Shall I hide from Abraham what I am about to do, seeing that Abraham shall surely become a great and mighty nation, and all the nations of the earth shall be blessed in him? For I have chosen him, that he may command his children and his household after him to keep the way of the Lord by doing righteousness and justice, so that the Lord may bring to Abraham what he has promised him.” Then the Lord said, “Because the outcry against Sodom and Gomorrah is great and their sin is very grave, I will go down to see whether they have done altogether according to the outcry that has come to me. And if not, I will know” (Genesis 18:17-21, ESV).Thus, because of the covenant promises God made to Abraham, God reveals that He is about to destroy the wicked towns. Abraham intercedes by appealing to God's sense of righteousness: "Then Abraham drew near and said, 'Will you indeed sweep away the righteous with the wicked?'" (Genesis 18:23, ESV). And we know the story. God says He would not destroy the towns if ten righteous people could be found.
In one sense, Abraham's intercession worked. God agreed to his request. But in another sense, it failed because the towns were destroyed anyway. The people in the towns could not meet the requirements of the intercession.
Turning to Exodus, we see a similar setup. God first establishes the covenant in Exodus 24:
Then he [Moses] took the Book of the Covenant and read it in the hearing of the people. And they said, “All that the Lord has spoken we will do, and we will be obedient.” And Moses took the blood and threw it on the people and said, “Behold the blood of the covenant that the Lord has made with you in accordance with all these words” (Exodus 24:7-8).Moses then goes up Mount Sinai for forty days and nights, and the Israelites immediately make a golden calf and worship the idol. Thus we read:
And the Lord said to Moses, “Go down, for your people, whom you brought up out of the land of Egypt, have corrupted themselves. They have turned aside quickly out of the way that I commanded them. They have made for themselves a golden calf and have worshiped it and sacrificed to it and said, ‘These are your gods, O Israel, who brought you up out of the land of Egypt!’” And the Lord said to Moses, “I have seen this people, and behold, it is a stiff-necked people. Now therefore let me alone, that my wrath may burn hot against them and I may consume them, in order that I may make a great nation of you” (Exodus 32:7-10, ESV).Just as with Abraham, God informs Moses that He is about to destroy a people. And just like Abraham, Moses intercedes:
But Moses implored the Lord his God and said, “O Lord, why does your wrath burn hot against your people, whom you have brought out of the land of Egypt with great power and with a mighty hand? Why should the Egyptians say, ‘With evil intent did he bring them out, to kill them in the mountains and to consume them from the face of the earth’? Turn from your burning anger and relent from this disaster against your people. Remember Abraham, Isaac, and Israel, your servants, to whom you swore by your own self, and said to them, ‘I will multiply your offspring as the stars of heaven, and all this land that I have promised I will give to your offspring, and they shall inherit it forever.’” And the Lord relented from the disaster that he had spoken of bringing on his people (Exodus 32:11-14, ESV).The sins of Israel were, in some ways, far worse than the sins of Sodom and Gomorrah here. After all, the Cities on the Plain had never had a covenant with God; they had never agreed to be obedient to Him. Israel had agreed to that, and they had within days turned from the LORD. They had literally just seen the gods of Egypt crushed by the might of Yahweh, and fashioned their idol out of the jewelry they had looted from the broken Egyptians who begged them to leave.
But also notice here how Moses’s intercession differs from Abraham’s intercession before Sodom. Abraham appealed to the righteous, and God agreed He would not destroy the righteous along with the wicked. Moses appealed to God’s Name, which He had given to His people, before the country of Egypt. After having saved Israel with His might, would the Egyptians get the last laugh as God destroyed the people He had just "saved"? Not only that, Moses also appealed to the very covenant God had made with Abraham, and reaffirmed with Isaac and Jacob (called here by the name of Israel, which does refer to the person and not the nation). It was God’s promises that Moses presented as the basis for mercy.
Abraham’s appeal did not ultimately work because there were not even ten righteous people in the town of Sodom. Moses, by not relying upon the goodness of the people involved, actually succeeded in having God not destroy the nation of Israel because he relied not on the inherent goodness of the people of Israel (who had already proven themselves to be evil), but instead upon the promises that God had made, that He would bless the nation of Israel.