Isaiah 11-12 is the conclusion of a major section of Isaiah that began in chapter 2. This section begins and ends with the eschatological reign of the King over Israel and the nations. In chapter 2 the king is identified as Yhwh; in chapter 11 he is identified as Davidic. In between Isaiah provides evidence that he is both God and man in one person. This major section can be divided into three sub-sections: 2-5, 6, 7-12.
Isaiah 9:8-10:4 describe the judgment that God would bring on Israel and Judah through Assyria. Isaiah 10:5-19 then reveals that once God is finished using Assyria to judge Israel and Judah, God will then judge Assyria for its wrongdoing.
However strong may be the connections of theme or wording with the previous passage, the opening phrase of 10:33 clearly marks the start of a new literary unit, as its comparable use in 3:1 shows (הנה + this particular elaborate form of the divine title + participle); indeed, here it even lacks the editorial conjunctive כי that we find there. Suggestions that the section should begin as early as 10:27 (e.g. Blum, ‘Jesajas prophetisches Testament’, 567, with previous literature documented; Roberts) cannot, therefore, be entertained. Equally clearly, והיה ביום ההוא in 11:10 (see on 7:18) indicates the start of the next unit, there being no indication of any break in between.
Williamson, ICC, 629.
Based on Williamson’s comment and reflections from Bauckham’s essay (“The Messianic Interpretation of Isaiah 10:34,” in The Jewish World around the New Testament [Grand Rapids: Baker, 2008]), this is how I would see these verses in context.
10:5-11 – Assyria is God’s rod against his people, though Assyria does not understand this.
10:12-14 – Assyria boasts of itself
10:15-19 – God will judge proud Assyria
10:20-23 – The eschatological promise of a returning remnant of Israel
10:24-27 – Application of the preceding teaching to Israel when the Assyrians come against them.
10:28-32 – A description of Assyria’s march through Israel to Jerusalem.
10:33-34 – The curtain is pulled back; God is the one lopping the boughs of Israel and bringing the lofty low and cutting the thickets of the forest with an axe. – Note that the axe imagery links back to 10:15—Yhwh wields the axe (Assyria) against Israel.
11:1 – Though God has hewn the lofty in Israel down, a shoot will come forth from the stump of Jesse.
Bauckham understands John the Baptist to allude to these passages, with the understanding that the Majestic One is the Messiah. Given the above understanding, if Bauckham is correct, John is not working from a direct messianic prediction in his allusion to 10:33-34. Instead, he is alluding to a historical judgment of the Lord Yhwh on Israel in the past and warning that the Messiah will bring such a judgment against Israel in the future if they do not repent.