The Boston Globe’s biggest union says it has met the New York Times Co.’s requests in order to keep the paper running.

But as of early this morning, there was no indication of whether those concessions would be enough to end the threat of closure.

The Times had given the Boston Newspaper Guild until midnight Sunday to agree to cuts of roughly $10 million, which the union says it did despite what it termed “bullying” tactics by the NYT Co. in threatening to proceed with the shutdown.

The Times Co., for its part, said a deal was still being negotiated as of early this morning, and it sent a copy of its proposed 60-day shutdown notice to the union.

The notice would be filed, the Times said, if all the Globe unions did not agree to $20 million in cuts, half of them from the BNG.

One issue apparently is the inclusion of a lifetime job guarantee clause, which protects workers from being let go without cause. The BNG worries that eliminating the clause would make older, higher-paid workers vulnerable to layoffs.

The recent economic downturn has been especially hard on the Globe, which the Times Co. acquired in 1993. After posting an operating loss of $50 million last year, the paper is forecast to post a loss of $85 million this year.

Negotiations with other Globe unions have also resulted in concessions. The mailers union said it had agreed to cuts of $5 million, while drivers okayed cuts of roughly $2.5 million, according to a story in today’s paper. The pressman’s union, like the BNG, remains in negotiations.