The annual defense authorization bill sailed through both chambers of Congress, but the issue of military detention for terrorism suspects remains unresolved for scores of lawmakers.

The House approved the $662 billion defense bill on Dec. 14, and the Senate followed suit the next day. Yet despite passing with strong majorities, follow-up bills have been introduced by many Members  to address the measure’s detainee provisions, which at one point prompted a veto threat from the Obama administration before lawmakers made tweaks to satisfy the administration.

Rep. Jeff Landry (R-La.), who voted for the defense authorization conference report, said “there still is a great amount of concern” that has prompted Members to introduce follow-up legislation.

“At the end of the day, Congress is granted the right to rip the very liberties and freedoms from American citizens if it so chooses to,” Landry said. “That’s a decision that should be clear and precise, and it’s one of the responsibilities that should be taken serious.”

Landry introduced legislation the day after the House approved the defense measure that would prevent Americans from being detained indefinitely without trial. Several Republican lawmakers shared Landry’s concerns and GOP leaders nearly pulled the vote from the floor because of the outcry. That vote went on as scheduled but skepticism about the issue of military detention for American citizens suspected of terrorism remains.

Freshman Rep. Trey Gowdy (R-S.C.), who voted “no” on the defense bill, said the hourlong conversation at a GOP Conference meeting just before the House floor vote showed “there is a sufficient lack of clarity that it needs to be clarified.”

“I just think when you’re dealing with the Constitution you should have as much clarity as you can,” Gowdy said. “I think the fact that there are bills being introduced to make it more clear probably should signal to the people who drafted it that there wasn’t sufficient amount of clarity.”

The House Armed Services Committee issued a release after the House floor vote titled “Dispelling Myths and Misinformation About (the National Defense Authorization Act),” which, among other things, asserted that the approved measure “adds explicit protections for American citizens — even American citizens who have joined al-Qaida to take up arms against the United States.”

On the Senate side, a bipartisan group of Members has also voiced its displeasure with elements of the annual defense authorization that in most years draws a broad bipartisan majority. Intelligence Chairman Dianne Feinstein, who voted “yes,” unveiled a bipartisan measure after the Senate vote that, like Landry’s House bill, would prevent the indefinite detention of American citizens.

The California Democrat also tried to strike a compromise on detainee language between the Senate and White House  when the chamber first debated the defense measure, but Obama issued a veto threat despite her efforts. The White House finally lifted that threat after conferees worked out their measure to ensure there would be no interference with FBI investigations.

Even the White House had its own misgivings about the bill. In his statement announcing the end of the veto threat, White House Press Secretary Jay Carney noted that “if in the process of implementing this law we determine that it will negatively impact our counterterrorism professionals and undercut our commitment to the rule of law, we expect that the authors of these provisions will work quickly and tirelessly to correct these problems.”