There is a tendency today to view prophecy as simply a concrete prediction concerning future events. But the "this is that" approach misunderstands the role that Scripture plays and underestimates the sophistication of both the Old and New Testament authors.
Prophecy is not only (or even primarily) a prediction of future events. The primary role of a prophet is not to reveal specific details about the future. A prophet of God is divinely inspired with more than ordinary spiritual insight, one who hears from and speaks for God. He (or she) provides divinely inspired instruction, exhortation, warning, encouragement, and, at times, specific prediction.
The New Testament writers, including Paul, the evangelists, Peter, John (in Revelation), and the anonymous author of Hebrews use Isaiah extensively. In particular they quote, paraphrase, echo, and adapt from among the oracles in 13-39. Outlining a large number of examples in this chapter, Ben Witherington demonstrates that the New Testament view of the prophecies in Isaiah is not a simple "this is that." Rather their approach is far more complex. Paul, for example, sees Isaiah speaking both to ancient Israel and into the context of Paul's first century experience. Concerning Romans 9, Witherington writes:
Paul is able to use the text of Isaiah in the way he does not only because he believes it is the word of God, but because he believes those prophecies of old were indeed open-ended, poetic, and metaphorical in character, having depths of meaning that even Isaiah himself had not probed. (p. 153)
Among other things, Paul takes the imagery of God as potter in Isaiah and in Jeremiah and uses it to make his specific point.
The prophetic writing in Isaiah can at times be explicitly eschatalogical - speaking into the distant future, although in general rather than specific terms. The New Testament authors appreciate this and pick up on it with application to their present - or to our more distant future.
In other places the the text is understood to have had a concrete application in Isaiah's day (ca. 742-686 BC), but still be applicable in the 1st century and beyond. After all, God has not changed - his expectations of his people remains constant. (Summarized briefly: Love the Lord your God with all your heart, mind, soul, and strength and love your neighbor as yourself.) His kingdom will come.
We can see an example of this in Paul’s use of Isaiah 29:14 in 1 Corinthians 1:19:
NIV and Masoretic Text (MT) Therefore once more I will astound these people with wonder upon wonder; the wisdom of the wise will perish, the intelligence of the intelligent will vanish. (29:14)
Septuagint (LXX) Therefore look, I will proceed to remove this people, I will remove them and destroy the wisdom of the wise and the discernment of the discerning I will hide.
Paul quotes this as:
For it is written: “I will destroy the wisdom of the wise; the intelligence of the intelligent I will frustrate.”(1 Cor. 1:19)
Ben Witherington notes that Paul changes the final word in his quote – presumably because it better suits his purpose, but he is also using the quote in a manner that is consistent with its initial use by Isaiah.
While Paul surely knows that the judgment being rendered in Isaiah 29 is in the first place on ancient Judean leaders in Isaiah’s day, he believes it is also an apt “indictment of the rhetorical affectations of the Corinthians.” Paul believes that the prophetic word has the same meaning as it did, originally talking about God’s critique and correction of mere human wisdom, but he thinks it has an equally suitable application in his own day to his Corinthian converts. In this case, this is not about multivalency, but about enduring truth that has many applications in many eras. (p. 157)
Isaiah spoke prophetically warning and exhorting his people in his day. This was not a prediction of what God would do in first century Corinth (or 21st century America). But it captures an enduring truth that had application as a warning and exhortation in the 1st century and still has such application in the 21st century.
More broadly, Isaiah foretold that God exercises judgment and mercy and that his plans for Israel, and indeed all of humankind, will ultimately prevail. What does this mean? Most importantly, it means that the New Testament authors are not using Isaiah as a source of proof texts applied to Jesus.
Witherington summarizes the important points and rather than trying to paraphrase his summary, I quote segments of it here:
It is only when we too narrowly estimate what is going on in the use of Isaiah in the NT that we draw the wrong conclusions. It’s not all about a “this is that” here’s the prediction and here’s the literal fulfillment hermeneutic, though sometimes the OT is used that way in the NT. Sometimes an author may simply use resonant Isaianic language to make a different point, call it a rhetorical or literary use of Isaiah. Sometimes the author may echo the larger context of an Isaiah passage, reflecting a knowledge of the importance of the original context, but sometimes this is not the case. Sometimes the NT author may cite the version of the OT text of Isaiah which best makes his point. Usually this involves the LXX, but sometimes, as in Revelation, it appears to involve dependency on the Hebrew text. In any case, the NT authors are happy to affirm that even the Greek translation of the OT is God’s word, which can be applied in various ways to their audiences. (p. 169)
The New Testament authors used the book of Isaiah in a wide variety of ways, and it is important that we recognize these. He goes on to outline two important ways that they read Isaiah (and other Old Testament books) with "christological and eschatological glasses." This is appropriate ...
Because in the first place there is a surplus of meaning, a polyvalence, in the poetic language of Isaiah’s prophesies. It is a language based in metaphor, in rhetorical hyperbole, in vivid images, which, since it involves the use of analogy, invites one to use it in fresh ways in different contexts. The meaning of the text is to a certain degree open-ended, or to put it another way, not confined to its original context, especially when Isaiah speaks about the more remote future, which he does on occasion.
Second, and just as important, Isaiah himself is interested in the subject of the final redemption of God’s people after they have suffered judgment. He is interested in the issue of royal rule and things we would call eschatological—the overcoming of death, perhaps even by means of bodily resurrection. There are glimpses of the future discussion of such things in Isaiah’s oracles, and precisely because they often involve grandiose language (e.g., a return to Eden) they invite a later filling out of their senses and an application to a time and place and person that more nearly fits the glorious description given. … The past is not just prologue, in the view of the NT writers the past is preparation, a building of the foundations on which the chief cornerstone can be laid later.” (pp. 169-170)
God’s mission in the world, his work through Israel, Jesus, and the church is one continuous story. While Isaiah doesn’t contain a hidden message - it isn’t a compendium of proof texts that can used to validate Jesus - the God who communicated to Judea through Isaiah remains constant. There is an enduring truth in the message. Jesus, through his life, death, and resurrection is a fulfillment of Isaiah’s vision of “final redemption and royal rule.” Paul and the other New Testament writers recognized this and used Isaiah accordingly.