The House of Judah is already cut off from the Spiritual Tree. Like everyone, it is only by accepting Jesus, that Jew and gentile can be grafted in.
The basic problem of who is Israel, is coloured by the false 'rapture' of the Church to heaven, before any turbulation. For this wrong theory to work, there must be an Israel on earth undergoing the great Trib. This belief then has the Jews mass converted when Jesus Returns.
That this whole scenario is false and impossible, is easily proved by careful study of all the Prophesies.
I disagree that the "house of Judah" is cut off. Remember what Apostle Paul taught in Romans 11 about his brethren the unbelieving Jews which God spiritually blinded away from The Gospel. It ain't over until the fat lady sings, so to speak. So the Jews today still represent the old "house of Judah", otherwise how are the two sticks of Ezekiel 37 going to be joined back together when Jesus comes if there is no more "house of Judah"?