President Barack Obama is prepared to veto the fiscal 2017 defense authorization bill if it includes a provision that the White House believes would allow some forms of discrimination in federal contracting.

So said senior administration officials at a White House meeting Monday of groups that oppose the provision, according to participants in the conclave who requested anonymity to talk about it.

The White House has not publicly and explicitly vowed to veto the $600 billion-plus defense bill over the House-passed provision by Oklahoma Republican Steve Russell. But the administration officials told their allies Monday that they have delivered just that message privately to members in unequivocal terms. White House Chief of Staff Denis McDonough has personally reached out to key lawmakers on the issue, the administration officials said at Monday’s meeting.

Word of McDonough’s lobbying and the White House’s firm position on the Russell provision highlights the seriousness with which critics take the amendment. And the intensity of that lobbying underscores how the fate of the authorization measure, which has been enacted every year for more than half a century, may hinge on the matter.

In fact, Senate Democrats are not ruling out blocking floor action on the authorization bill if the Russell language is not removed.

Another possible trigger for a presidential veto: if the final bill contains language that restricts the president’s ability to close the U.S. military-run prison at Guantanamo Bay, Cuba, officials said at the meeting. The White House has previously said this in public, but the message delivered behind closed doors on Monday shows the concern is still a live one.

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The Russell amendment is one of only a few issues snagging talks to write a final fiscal 2017 defense authorization measure, said Rep. Adam Smith of Washington, top Democrat on House Armed Services, in a brief interview with CQ Roll Call in late September.

According to critics, the amendment, adopted by House Armed Services in May, would permit religiously affiliated contractors that do business with any government agency to discriminate against employees based on the religious views of the employer. This could endanger employees who are gay or who got pregnant out of wedlock, for example, critics say.

Russell has countered that his amendment is only intended to ensure the 2,000-odd religiously-affiliated federal contractors don’t have to violate their core beliefs to do business with the government.

“We are accused of hatred, called out as shameful, and enjoined to use the whole Constitution to support an opposing view that embodies behavior, mores and outcomes that not only violate our conscience, but have been prohibited under the laws of nature and nature’s God,” Russell said in a May House floor speech.

News of the White House lobbying push comes on the same day as fully 42 Senate Democrats — enough to sustain a filibuster — wrote Armed Services leaders urging them to ensure the Russell provision, or Section 1094 of the House bill, is not included in the conference report.

“If enacted,” the letter says, “Section 1094 would vastly expand religious exemptions under the Civil Rights Act and the Americans With Disabilities Act to allow religiously affiliated organizations receiving federal funds to engage in discriminatory hiring practices—using taxpayer dollars to harm hardworking Americans who deserve to be protected from workplace discrimination based on sexual orientation, gender identity, religious identity, or reproductive and other healthcare decisions.”

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Sen. Richard Blumenthal, D-Conn., who helped organize the letter, declined to say Tuesday whether Democrats would block the NDAA from moving forward if the Russell amendment is attached to the final version.

“I have never voted against a National Defense Authorization Act, and I am very, very hopeful that I will vote for this one,” Blumenthal said on a conference call with reporters. “What we’re trying to do here is eliminate this provision before the NDAA reaches the floor. Clearly there are enough signers here to indicate that there is a possibility that the bill could be blocked at least temporarily. But we have not explicitly said we would. Certainly if the bill reaches the floor we will have to consider all the options.”

Monday’s White House meeting on the Russell amendment was led by two presidential assistants: Paulette Aniskoff, director of the Office of Public Engagement; and Amy Rosenbaum, director of legislative affairs.

Representatives of several outside groups that are allied with the White House on the Russell issue were in attendance. These included Planned Parenthood, the Center for American Progress, the Human Rights Campaign, the American Civil Liberties Union, the National Women’s Law Center and Americans United for Separation of Church and State.

The White House’s Statement of Administration Policy on the House bill, issued in May, listed the Russell amendment as a top concern. But the document did not directly state that the Russell provision, or any particular section of the measure, would trigger a veto.

Emily Horne, a White House spokeswoman, would not provide additional clarity on what might trigger a veto. Nor would she discuss details of the meeting or White House advocacy efforts.

Niels Lesniewski and Bridget Bowman contributed to this story.