But McKeon said Tuesday night that the language is "similar" to the Obama administration's interpretation of the Authorization for Use of Military Force resolution that was approved in September 2001, just a week after the 9/11 attacks. He also said it is important for Congress to update its thinking on the use of force against terrorist groups for the sake of U.S. troops.

"I believe our men and women in uniform deserve to be on solid legal footing as they risk their lives in defense of the United States," he said.

The White House on Tuesday said it broadly supports the NDAA, but said it has concerns with some of the language in it, including Section 1034. The White House Statement of Administration Policy said this section would "effectively re-characterize its scope and would risk creating confusion regarding applicable standards."

This is just one area of concern for the administration, which also said it objects to House GOP language in the bill that would delay the end of the military's "Don't ask, don't tell" policy regarding gay service members.

The House debated the NDAA for an hour Tuesday night, and is expected to begin consideration of amendments on Wednesday.