In his discussion of ten key issues where the Dead Sea Scroll are relevant to historical Jesus studies ["Jesus and the Dead Sea Scrolls" in Doris Donnely (ed.), Jesus. A Colloquium in the Holy Land with James D.G. Dunn, et al. Continuum, 2001. Pp. 27-44], Harrington briefly considers Jesus' teaching "no divorce":
By the criteria of dissimilarity and multiple attestation, the prohibition of divorce belongs to the corpus of Jesus' authentic sayings. It went against Jewish practice and even against the permission of the Scriptures (Deut. 24:1-4), and it appears in Mark (10:2-12), Q (Luke 16:18 and Matt. 5:31-32), and 1 Corinthians (7:10-11). Of course, one must take account of the exceptions introduced by Matthew (see Matt. 5:32 and 19:9) and Paul (see 1 Cor. 7:12-16). One must also ask how Jesus intended this teaching to be taken---whether as an ideal, a legal principle, a protection for women, a temporary measure (in the face of the coming kingdom of God), or whatever else. Nevertheless, it is fair to say that Jesus taught "no divorce."
After a brief reference to the well-known debates between the rabbinic traditions associated with Hillel, Shammai and Aqiba, Harrington (page 38f) cites two Qumran texts on the issue:
Damascus Document 4:20-5:6 declares that "taking a second wife while the first is alive" is fornication. ... The problem here, however, is that the topic at issue seems to be polygamy rather than divorce and remarriage, as the rest of the passage with its concern to explain David's several wives suggests.
The Temple Scroll (11QTemple) contains a long section about the king. With regard to marriage (57:15-19), the ideal king should marry within the royal household of Israel. The text goes on to say: "He shall not take another wife in addition to her, for she alone shall be with him all the time of her life." Again the "no divorce" interpretation is problematic. The first problem is whether the directive applies to anyone beyond the king. And the second problem is whether it refers to polygamy on the king's part or to divorce and remarriage, though here the evidence for "no divorce" is stronger.