Cosmo Macero, a spokesman for the Newspaper Guild, said the union and management stopped negotiating at about 8 a.m. and "should resume in the next day or so."
He did not have additional information.
The paper's three other unions - representing mailers, delivery drivers and pressmen - all reached tentative agreements Monday morning, according to CBS Station WBZ.
The mailers union agreed to $5 million in concessions, while the delivery drivers agreed to about $2.5 million in concessions.
The Globe's owner, The New York Times Co., has threatened to close the newspaper unless the unions agreed to $20 million in cuts.
The paper reported $50 million in operating losses last year, and is projected to lose $85 million this year.
Management said it has given its biggest union a copy of a notice it was prepared to file Monday if it were unable to reach an agreement on the concessions by midnight Sunday. The 60-day shutdown notice is required under federal law.
The Boston Newspaper Guild called the move a "bullying" tactic, and said in a statement that the proposed cuts represented "tremendous sacrifices, across virtually all categories of compensation and benefits."
CBS News correspondent Randall Pinkston reports that the troubles at the Globe coincide with tough times for the nation's media outlets. Ad revenues are in freefall as newspapers and magazines lose subscribers, while readers have come to expect free content on the Web.
This year alone, the Rocky Mountain News, and the and Christian Science Monitor in Boston have gone Web-only.