If the dough offered as firstfruits is holy, so is the whole lump.
After Elijah is through with the contest of the prophets at Mt Carmel (1 Kings 18), he realizes that Jezebel who had been persecuting the prophets of Adonai does not appreciate getting some of her own 'medicine'. Discouraged and feeling that in spite of these glorious events, he was unsuccessful in bringing Israel back to her God, Elijah retreats in the desert and complains to God, "It is enough; now, O LORD, take away my life, for I am no better than my fathers." God denies Elijah the desired death but instead sends an angel to strengthen him. (Aren't we thankful for unanswered prayers sometimes?) The weary prophet then decides to return where it all started Mt Sinai. There he has conversation with the 'Word of the Lord'' who came to this prophet of doom and gloom in the 'still small voice'. The 'Word' then opens Elijah's eyes to see a 7,000 faithful man remnant for whose sake God will not destroy Israel (1 Kings 19: 1-18).
This remnant principle is a very important one in the redemption program. Abraham understood it and even used it when pleading for the life of his nephew Lot. There Adonai who would destroy Sodom said, "For the sake of ten (righteous people) I will not destroy it."
In his thesis on the subject of God not rejecting Israel in spite of unbelief, at the time when the Roman noose gets tighter and tighter around Israel, Paul comforts himself and others reminding us all of this remnant principle. At that time in Paul's mind the remnant is the Jewish growing community of believer. For their sake he says God had not rejected Israel (Romans 11:1-4). This represents a very different theology than the usual one claiming that God rejected His people to replace them with another.
Even so in these ends of time Israel at large along with the world is sanctified before God by the 144,000 remnant of believers from all the tribes of Israel. They are called the 'firstfruit ' for the Lamb who is himself a 'firstfruit of those who have fallen asleep' (Corinthians 15:20; 15:23; Revelations 7:4; 14:4) Yes, If the dough offered as firstfruits is holy, so is the whole lump, and if the root is holy, so are the branches (Romans 11:16). From the beginning it was, is, and shall always be: redemption by representation.
Another reality is that like 'Yeshua the Firstfruit', the firstfruit is also the one who takes the brunt of the punishment for the nation. Even though it did nothing to deserve such a fate, as the firstborn, it is consecrated to God and sometimes offered as an offering for the sanctification of the rest. May we when the time comes be willing offerings after the sample of the Master (Romans 12:1).