House Republican leadership is actively discussing new ways to restrict the classified information that all lawmakers can receive, after the White House indicated it will limit intelligence sharing with Congress going forward. Democrats are warning that would threaten their ability to do their jobs, and some Republicans also say they would be against further restrictions. The conversations happening at the House leadership level have so far revolved around who should be allowed to access the most sensitive information, lawmakers involved in the discussions told CNN. The Trump administration is planning to limit what it shares with Congress, a senior White House official told CNN on Wednesday. That comes afterCNN reportedthat, according to an early US intelligence assessment that was described by seven people briefed on it, the US military strikes on three of Iran's nuclear facilities did not destroy the core components of the country's nuclear program and likely only set it back by months. "We're looking into that," House Speaker Mike Johnson told CNN, when asked what ways he is looking to limit classified information coming to Congress in the future. "It's a real problem." Johnson did not rule out eliminating classified briefings for the entire House, which House and Senate lawmakers received last week on Iran, as a potential option. "It probably affects what we are able to be told because there are real risks to that. So, it's unfortunate. It effects how the institution works, and that's a problem so we got to address it," Johnson said. House Homeland Security Committee Chair Mark Green confirmed to CNN that "there's a debate" among House GOP leadership over how to institute new restrictions. Green said some of the ideas include restricting classified information to just key committee chairman and the "Gang of Eight," which is made up of the congressional leaders from each party and the top Republican and Democrat on the House and Senate intelligence committees. House Intelligence Committee Chair Rick Crawford told CNN on Thursday he is already taking "proactive steps" to manage classified information on Capitol Hill, without divulging specifics. In response to restrictions under consideration, one Republican lawmaker who does not serve on the Intelligence Committee and whom CNN granted anonymity to speak freely said, "I would personally resist loudly if my access was limited." There are limits to what Republicans can do to implement new stipulations on classified information sharing. USlawrequires the intelligence community "keep the congressional intelligence committees fully and currently informed of all intelligence activities, including any significant anticipated intelligence activity." The potential to limit the sharing of classified information will most likely impact rank-and-file lawmakers who don't sit on relevant committees of jurisdiction, setting up a situation where the majority of Congress would potentially be left in the dark on key matters of national security unless they were explicitly told. The White House on Thursday declined to say how it would be limiting the classified information it shares with Congress or how it would respond to lawmakers who maintain their oversight duties necessitate access to the information. "This administration wants to ensure that classified intelligence is not ending up in irresponsible hands, and that people who have the privilege of viewing this top-secret classified information are being responsible with it," White House press secretary Karoline Leavitt told reporters at a briefing. "And unfortunately, clearly, someone who had their hands on this — and it was a very few people, very few number of people in our government who saw this report … that person was irresponsible with it," Leavitt added, referring tothe early Defense Intelligence Agency assessment. CIA Director John Ratcliffehas saidthat "a body of credible intelligence" indicated Iran's nuclear program was "severely damaged" by the US strikes and that "several key Iranian nuclear facilities were destroyed and would have to be rebuilt over the course of years." While it was not clear whether Ratcliffe was offering an official agency assessment or his view of the intelligence, it's not unusual forintelligence agencies to disagree when making a judgment call about how to interpret raw reporting. The analysis of the damage to the sites and the impact of the strikes on Iran's nuclear ambitions is also ongoing, and could change as more intelligence becomes available. While Democrats have condemned the leak, they have warned Republicans against taking any steps to restrict classified information. The top Democrat on the House Intelligence Committee, Jim Himes, said in a statement to CNN that it is "unacceptable for the administration to use unsubstantiated speculation about the source of a leak to justify cutting off Congress from classified intelligence reporting, particularly when over a million people within the Executive Branch have clearance to access classified top-secret reporting." Democratic Rep. Rosa DeLauro, the highest-ranking Democrat on the House Appropriations Committee, said intelligence is already limited on Capitol Hill and restricting it further could inhibit lawmakers from being able to do their jobs. "If you don't have information then you are moving against a democratic process and you're constraining government. Government is not operable if you don't have the information you need to vote," she told CNN. The active discussion has forced Republican lawmakers to confront the precedent they want to set going forward and how comfortable they are with the possibility of taking themselves out of the information sharing equation under a Democratic presidency in the future. GOP Rep. Brian Fitzpatrick, who serves on the House Intelligence Committee, told CNN "of course" he is worried about the precedent being set if classified information is further restricted to lawmakers on Capitol Hill, but added, "I worry about leaks too." For members who don't sit on the key intelligence committees, like GOP Rep. David Valadao, there is a concern over what it would mean to be in the dark. "The thing that we deal with in Congress is we never know what we don't know," Valadao told CNN. GOP Rep. French Hill, another House Intelligence Committee member, told CNN he would prefer that Johnson and his team focus on enforcing the current restrictions around intelligence sharing, rather than creating new ones. "We have significant rules now," Hill said. The discussion over restricting access to information sharing has also created opportunities for Democrats to argue that the details the Trump administration has shared about the US strikes on Iran are being politicized and cannot necessarily be trusted. That dynamic was on full display on Thursday when Senate Republicans and Democrats emerged from an hourlong administration briefing on the US strikeswith conflicting accountsof what the briefers said. A significant number of Republicans, however, say restricting the access lawmakers have to classified information is a good thing because they argue many cannot be trusted. House Ethics Committee Chair Michael Guest, who supports limiting classified information to just key party leadership and intelligence committee leaders, said, "I believe there's a lot of the information, as far as rank-and-file members, that when we receive it, it very quickly finds a way to leak its way out into the public." "I wouldn't tell any member of Congress anything classified if you didn't want people to know," GOP Rep. Tony Gonzales, who spent 20 years serving in the military, told CNN. "The really sensitive stuff, there's no need to know. All of the other details, it comes out so fast." Fitzpatrick shared that briefers have come before the House Intelligence Committee and shared they are afraid to be fully honest because they don't trust Congress' ability to protect classified information. "That's a problem," Fitzpatrick added. Rather than cutting all members off from classified information, GOP Rep. Austin Scott, another member of the House Intelligence Committee, said lawmakers should go through a background check to understand the gravity of the material they would be seeing. "The fact that by virtue of being elected to Congress you get to see classified and hear classified information, I think those days have long passed," Scott told CNN. For more CNN news and newsletters create an account atCNN.com