“It’s a separate conversation whether a lot of this stuff is over-classified — that’s probably true. And it’s a separate conversation about whether or not this administration has misled the public about what’s happening in Ukraine — that’s probably true,” Hawley said.

The influential conservative added that claims Teixeira has “exposed stuff the public should know’” might be “fair enough, but is the way he did it the right way to do it? No.”

As lawmakers received their first detailed classified briefing on the case Wednesday, the degree to which Greene stands alone marks a significant line in the sand for a Republican Party that’s increasingly split over commitment to defending Ukraine against Russia. Regardless of their stance on the Ukraine war, and on over-classification across the government, GOP lawmakers across the ideological spectrum agree that Teixeira should be held to account.

“They’re on an island with regard to serious policy people,” Sen. Kevin Cramer (R-N.D.) said in an interview regarding Greene and Carlson. “Unfortunately, they’re on an island of influence. But there’s not a lot you can do about that.”

The FBI arrested Teixeira over his alleged involvement in the leak of the classified documents last week. The documents included sensitive intelligence on Ukraine’s spring plans in its war against Russia, as well as a trove of other information on global hotspots. Teixeira has since been charged with two federal crimes over his actions, which have attracted attention from the highest levels of the federal government.

Senators left their briefing saying it revealed little new information. But many suggested the scope of the breach indicated Congress would have to step in to revamp how the federal government handles classified information. Majority Leader Chuck Schumer told reporters he thought “there have to be some improvements” without elaborating what those would be, and Intelligence Committee Chair Mark Warner (D-Va.) noted that “I think it’s time that Congress has got to step in.”

“I didn’t learn much more than they’ve already leaked,” Sen. John Kennedy (R-La.) said after the briefing, echoing the comments of other Republicans.

Senate Intelligence Committee Vice Chair Marco Rubio (R-Fla.) said he still had a lengthy list of questions and he “wasn’t satisfied with any plans they have in place to prevent this from happening in the future.”

“The core challenge we have on our hands right now is whether Congress is going to — on a bipartisan basis — assert not just our right, but our obligation, to come together to conduct oversight over these agencies, which we cannot do without full access,” he said. “It’s getting harder every day and cases like this make it even worse.”

Top officials who briefed lawmakers on the leak included Director of National Intelligence Avril Haines and others in the intelligence and defense communities.

Earlier Wednesday, Warner and Rubio sent a joint letter to Haines and Defense Secretary Lloyd Austin demanding a host of information about the leak. Among their requests: copies of all documents obtained and disseminated by Teixeira; details on why it took so long for the government to identify the leak; and whether the airman should have had access to the classified information.

Rubio said in an interview earlier in the week that time would reveal the leaker’s motives but added that his alleged actions were indefensible.

“It was illegal. It was a crime,” Rubio said. “I can’t be supportive of someone committing a crime.”

Greene, for her part, called Teixeira “white, male, christian, and antiwar” and asked who is “the real enemy” in an April 13 tweet. She moderated her defense slightly in a Monday appearance on Steve Bannon’s podcast, saying the leaker has “got to face some penalties for what he’s done — I’m not saying he shouldn’t,” but insisting that more of the U.S. actions in Ukraine should be exposed.

Carlson, in response to the leak, said at the top of his April 13 show that “telling the truth is the only real sin” in Washington.

Sen. Lindsey Graham (R-S.C.) was the first to publicly bash Greene, accusing her of making “one of the most irresponsible statements you could make” in defense of the young guardsman.

And a flurry of congressional Republicans also made clear that viewing Teixeira’s alleged actions in the context of his criticism of U.S. involvement in the Ukraine war is a mistake, given that the leak endangered lives in various conflicts.

“In terms of defending him as a hero, he’s anything but that,” said Rep. Michael McCaul (R-Texas), chair of the House Foreign Affairs Committee. “He’s compromised our sources and methods. He’s compromised American lives on the ground — our assets on the ground that report intelligence to us.”

Even those Republicans skeptical of government actions in intelligence gathering wouldn’t back Greene’s position carte blanche. Sen. Rand Paul (R-Ky.) said he wasn’t familiar with the specifics of Teixeira’s case, noting it did not appear to be an “organized thing,” but said he saw it differently from that of Edward Snowden, whom Paul described as a whistleblower routing material through the media.

“There have to be rules about releasing information, but I think also there sometimes are hard questions,” he said in an interview, noting he was not making an analogy between the two cases.

Democrats, across the board, bashed Greene and Carlson for offering any sort of political cover for the actions of the leaker.

“I don’t know which nation-state they’re loyal to,” Warner said.

Lawmakers on both sides of the aisle are broadly interested in revisiting how much information is classified by the federal government, as well as how many people have access to it, in light of Teixeira’s alleged leaks. They predicted the episode would inject bipartisan momentum into legislation revisiting classification procedures.

In addition, Congress has begun to investigate the leaks. House Armed Services Chair Mike Rogers (R-Ala.) and Intelligence Chair Mike Turner (R-Ohio) pressed the Defense Department for information about the disclosures in a Tuesday letter.

While that oversight moves ahead, Republicans broke from Greene to argue that the leaker must be punished as harshly as possible, regardless of what any loud voices on their party’s right might suggest.

“If you leak classified documents, you’re going to suffer consequences of the law,” Rep. Kevin Hern (R-Okla.), chair of the conservative Republican Study Committee, said in an interview. “Regardless of what the purpose is, we’ve made that statement for decades. We shouldn’t change that now.”

“Someone who does that needs to be punished to the full extent of the law,” Sen. Dan Sullivan (R-Alaska) echoed.

Asked about Greene and Carlson’s defense of his actions, Sullivan replied: “I stand by my statement. As someone who served in the military for almost 30 years, I know a little bit about what I’m talking about.”