In a letter delivered Tuesday to the leaders of the Armed Services committees, the lawmakers called the measure dangerous and urged that it not be included in the annual defense policy bill. They said the provision would amount to government-sponsored discrimination by permitting religiously affiliated federal contractors to refuse to interview a job candidate whose faith differs from theirs and to fire employees who marry their same-sex partners or use birth control.

But Republican proponents of the measure have described the provision as a bulwark for religious freedom.

Forty lawmakers, joined by two independents, signed the letter to Sen. John McCain, R-Ariz., and Rep. Mac Thornberry, R-Texas, the chairmen of the Armed Services panels.

The House added the provision to its version of the defense policy bill. The Senate did not, leading to a standoff. The divide could threaten the timely approval of the defense legislation, which authorizes military programs for the new fiscal year that started Oct. 1.

Congress returns after the Nov. 8 election for a lame-duck session and will be under pressure to resolve differences between the two chambers and get a final bill to the president’s desk.

Sen. Richard Blumenthal, D-Conn., who organized the letter, said Tuesday that a filibuster of the legislation would be an option if the provision isn’t removed before the bill reaches the floor of the Senate. But he said he’d hoped for a resolution before then.

The House provision was authored by Rep. Steve Russell, R-Okla., who said the provision is aimed at ensuring faith-based organizations that perform work for the U.S. government aren’t forced to act against their beliefs.

The committee’s top Democrats, Sen. Jack Reed of Rhode Island and Adam Smith of Washington state, also received the letter. But Republicans control deliberations over the bill, known formally as the National Defense Authorization Act.