Congress may consider legislation later this week that would scrap the Pentagon's COVID-19 vaccine mandate for military service members, Politico reports.

Why it matters: A rollback of the policy may be included in the National Defense Authorization Act, which is set to be unveiled Monday, as a compromise between Republicans and Democrats.

• Rep. Adam Smith (D-Wash.), chair of the House Armed Services Committee, told Politico Saturday a repeal had been considered but also that nothing had been decided yet.
• In August 2021, Secretary of Defense Lloyd Austin directed that all troops receive the coronavirus vaccine or face potential expulsion.
• Some Republican governors and members of Congress have argued that it's unfair to force troops to decide between getting the coronavirus vaccine or potentially being expelled from the military.

Austin said on Saturday that the policy should be maintained, saying, “We lost a million people to this virus,” according to AP.

• “A million people died in the United States of America. We lost hundreds in DOD. So this mandate has kept people healthy," Austin added.

What they're saying: House Minority Leader Kevin McCarthy (R-Calif.), who is vying to become House speaker in the incoming Congress, warned on Fox News Channel's “Sunday Morning Futures" that the bill would not move forward if the rollback is not included.

• McCarthy also said that he and President Biden brokered a compromise on the policy, though the White House later pushed back on those comments.
• Two top White House aides confirmed to the Washington Post on Sunday that Biden and McCarthy discussed the policy but that nothing is resolved.
• “Leader McCarthy raised this with the President, and the President told him he would consider it. The Secretary of Defense has recommended retaining the mandate, and the President supports his position. Discussions about the NDAA are ongoing,” White House spokesperson Olivia Dalton said in a statement to the Post.
• National Security Council spokesman John Kirby also told reporters on Monday that Biden agrees with Austin in opposing a repeal of the mandate.

Yes, but: The coronavirus vaccine is just one of several vaccines that service members are required to receive, as outlined in the "Joint Regulation on Immunization and Chemoprophylaxis for the Prevention of Infectious Diseases."

• Service members can request to opt-out of a mandatory vaccination on health, administrative or religious grounds, including the coronavirus vaccine.

The big picture: 21 Republican governors asked the Biden administration in a letter last week to repeal the policy, claiming the "unnecessary" vaccine mandate has hurt the armed service's recruiting efforts.

• Multiple factors account for the armed service's missed recruiting targets, including a tight labor market and competition with private companies, Army Gen. Joseph Martin, vice chief of staff for the Army, told Congress in July.
• As of Dec. 1, over 11,500 members of the Army, Army National Guard and Army Reserve had refused the COVID-19 vaccine, though 97% of the Army's active personnel received it.

Go deeper: National Guard falls short of target goals as troops continue to exit

Editor's note: This story has been corrected to reflect McCarthy was speaking on Fox News Channel's "Sunday Morning Futures," not on Fox Business Network's "Sunday Morning Futures."