The status of Jubilees in early Judaism is difficult to assess. Most of the scholarly energy on this text has been expended in establishing its text and origins -- both are fraught and problematic, although some broad consensus has emerged on Hebrew as the original language and roughly mid- or early-2nd C. BCE as the likely time of origin.
To answer the question directly, the best I can do is to quote a few sentences from James Vanderkam:
Apart from the Qumran texts, it is more difficult to trace the influence of Jubilees on later literature. ... While Jubilees seems to have had little influence later in Judaism, there is some evidence that it was known and used, although that evidence comes form relatively late times.
(The Book of Jubilees (T&T Clark, 2001), pp. 146-7.) The list of about a dozen texts that Vanderkam provides all come from the 10th C. CE and up (e.g., Bereshit Rabbati, Midrash Aggadah, etc.).
For the period of interest, that leaves the Dead Sea Scrolls (DSS) themselves as about the sole body of evidence, and there again the evidence is slender although significant. Vanderkam points out that the roughly 14 copies attested from among the DSS suggests "more than a little attention" in that quarter. He doesn't leave it completely vague, though:
That attention is evident in several places and in fact a good case can be made that at Qumran Jubilees was considered an authoritative writing, much like the books that would later be recognized as components of the Hebrew canon of Scripture.
(Book of Jubilees, p. 144). It appears that the Damascus Document (CD) cites it as an authority, and several other texts parallel or follow its content. Perhaps most intriguing is the way in which it relates to the Temple Scroll (11Q19). Jubilees "rewrites" roughly the book of Genesis, plus Exodus 1-19. The Temple Scroll basically picks up at that point, and covers (in some measure) the rest of Exodus-Deuteronomy (not reflecting all that content, however - the connections to the Deuteronomic Code are especially important).
The inference, then, is that at least among some segments of late Second Temple Judaism, Jubilees enjoyed a prominent status. Beyond this, however, one is speculating on the basis of the somewhat tortuous transmission of this document, and in a period well beyond that of first century Judaism.
Further reading - in addition to Vanderkam's work linked above:
- Geza Vermes, "The Book of Jubilees", in The History of the Jewish People in the Age of Jesus Christ, rev. and ed. by G. Vermes, F. Millar, and M. Goodman (T & T Clark, 1986), vol. 3.1, pp. 308-318. (For convenience and future reference: vol. 1; vol. 2; vol. 3.1; vol. 3.2).
- Michael Segal, The Book of Jubilees: Rewritten Bible, Redaction, Ideology and Theology (Brill, 2007) [Important recent study, very much oriented to questions of origins and authorship, so little attention later reception.]
- R.H. Charles, The Book of Jubilees, or The Little Genesis (A & C Black, 1902). [Scholarship has seriously moved on from Charles's work, but it remains in some ways fundamental. Although he is heavily criticized for things he omitted, still he is regarded as having shown good judgement in regard to the evidence that he did handle.]