There does not seem to be one view. It is taken either as having a “temporal” significance or an “eschatological” one by Amillenials.
The Non-Millenarian View 
This takes us to the third point, and that is the meaning of the
phrase “until the full number of the Gentiles has come in” (v. 25).
Most commentators agree that Paul’s use of “until” (achri) has
temporal significance and is intended to mark that period of time when Israel’s hardening ends and her fullness and acceptance
begins. Others, however, such as O. Palmer Robertson, insist
that the term has an eschatological significance and is indicative
of a condition that continues until the end. The key here is
Paul’s phrase “the full number of the Gentiles.” According to
Anthony Hoekema, “The fullness here . . . must be understood in an eschatological way: the full number of Gentiles God intends to save.
When that number of Gentiles has been gathered in, it will be the end
of the age.” Based on this interpretation, when the full number of
elect believers among the Gentiles has come in, then Israel’s hardness
will be removed, and Israel will attain the promised fullness and
acceptance shortly before the return of Jesus Christ. This
interpretation also comports with Jesus’s words that after God’s
judgment falls on Israel and her people are scattered among the
nations, “Jerusalem will be trampled on by the Gentiles until the
times of the Gentiles are fulfilled” (Luke 21:24). Once the times of
the Gentiles are fulfilled, God will remove Israel’s present hardness
of heart, and the nation will at long last return to her Messiah.
 “A case for Amilennialism”, © 2003, 2013 by Kim Riddlebarger Published by Baker Books a division of Baker Publishing Group P.O. Box 6287, Grand Rapids, MI 49516-6287 www.bakerbooks.com