In a town that feeds off legislative gossip, Sens. Lamar Alexander, R-Tenn., and Patty Murray, D-Wash., have been doing a really good job keeping private their negotiations on how to overhaul the No Child Left Behind law.

For nearly a month now, the chairman and ranking member of the Senate education committee have been working with their staffs behind closed doors to cobble together a bipartisan bill that would give the federal K-12 law a major facelift. But other than releasing a joint statement a few weeks ago announcing a planned committee markup of the bill during the week of April 13, the two have been mum on where their compromise stands.

That’s smart politics. After all, when they first announced they were going down this path, Alexander and Murray were far apart on a laundry list of education policy areas, including Title I portability, accountability, and early childhood education (more on that last piece here).

There’s one issue, however, that seems to flying under the radar: What to do about chronically low-performing schools. Should states have to identify a percentage of their poorest performers? Should they be allowed to craft a turnaround model themselves? And if they do craft their own models, should the Education Secretary get sign-off?

There’s a lot of wonky history behind those questions. When the Obama administration supercharged the School Improvement Grant program back in 2009, it limited the turnaround models to some pretty dramatic interventions, including removing the principal, replacing half the staff, converting the school to charter status, or shuttering it altogether.

What’s more, the administration essentially doubled down on that strategy in the NCLB waivers, which required states to identify the poorest-performing 5 percent of schools and put in place a turnaround plan that closely mirrors the SIG models.

But, members of Congress on both sides of the aisle have long pushed back on the Obama administration’s turnaround vision, arguing it’s too restrictive. And many felt their criticisms were bolstered when two successive years of student-outcome data from the SIG program showed that it has a decidedly mixed track record of actually improving schools.

Then, in January of 2014, lawmakers incorporated language into a spending bill for the U.S. Department of Education that added additional turnaround options to the mix, including allowing states to partner with organizations that have strong records of fixing low-performing schools, or to cook up their own turnaround options and submit them to the U.S. secretary of education for approval. And under new regulations, “priority schools” in waiver states were allowed to use those new models, too. The change was a big victory for many in Congress—and a blow to one of the Obama administration’s top priorities.

But, in a draft bill meant to spark discussion on an NCLB, Alexander signaled he’d like to go even further. The draft eliminates the SIG program entirely, instead allowing states to set-aside a greater share of their Title I dollars for school improvement. And there are no rules in the proposal about how many—or what kind—of schools states need to identify for improvement. The House GOP NCLB rewrite bill, which is still awaiting a floor vote after conservative criticism, takes an almost identical approach.

And over the past few weeks, there have been small signals that the turnaround question may be a point of contention between Alexander and Murray (not to menton the Obama administration, which will ulimately need to sign any compromise bill.) And we felt like it was high time to at least string them together, for whatever it’s worth.

So here are those bread crumbs:

Evidence #1: When the Senate began debating an anti-human trafficking bill, Alexander made a speech on the chamber floor on March 11 that focused on the overreach of the federal government. The crux of his speech wasn’t about education, but he quickly veered in that direction and started talking about how the U.S. Department of Education has overstepped its boundaries in regards to school turnarounds and the Common Core State Standards, and how that is one of many issues he’s currently negotiating with Murray.

“In No Child Left Behind, there are requirements about improving low-performing schools,” he said. “The [Education] Department, in its well-intentioned activities, defined what a Governor of Tennessee or Utah or Iowa could say about his or her own idea about fixing low-performing schools. That happens all the time. It happens all the time. Over the last several years we have created, in effect, a national school board in Washington, DC, by substituting the judgment of Washington for local schools.”

Evidence #2: In remarks to the press after meeting with members of the Council of the Great City Schools on March 16, President Barack Obama talked about the need to continue focusing on low-performing schools.

“We’ve got a major debate obviously taking place about the reauthorization of the major education act that shapes federal policy towards our schools,” Obama said. “There is, I think, some useful conversations taking place between the chairman of relevant committee, Lamar Alexander, and Patty Murray. But there’s some core principles that all the leaders here believe in: ... Making sure that we continue to focus on low-performing schools and that they are getting additional resources.”

Evidence #3: Days later, on March 19, Carmel Martin, the executive vice president for policy at the Center for American Progress, a think tank closely associated with the Obama administration and previously the assistant secretary of planning, evaluation, and policy development at the department, wrote an op-ed in the Washington Post about the success of targeted school turnarounds and why a rewrite of NCLB should include a federal role.

“Federal policy needs to keep the pressure on school districts and states to continue the momentum,” Martin wrote. “We have an opportunity to make great strides in improving educational outcomes, but passing a bill that does not include federal guardrails would be a step backward.”

Evidence #4: In an interview with Education Week on Monday, U.S. Secretary of Education Arne Duncan said he’s open to various different levels of federal involvement in turning around low-performing schools, but that an NCLB rewrite should include a role for the feds in school turnaround. Here’s what he said:

You’ve talked a lot about the federal role in turning around low-performing schools. Do you think there has to be a specific percentage of [schools states must identify as needing extra help]?

We need to not just label the problem, we need to not just admire the problem ... we need to do something about it. ... Some [schools] have done an amazing job with [turnarounds]. Some we haven’t seen as much as improvement as we’d like. But at least we’re trying. At least people are in the game. And to be clear ... we did 5 percent [a reference to the percentage of schools the education required states to identify for dramatic turnarounds]... there’s nothing magical [about that percentage]...whether it’s 4 percent or 6 percent ... we’re open to those conversations. ... We’re open on models ... you have to have evidence-based stuff. ... But let’s not just stand by. I promise you we would not be seeing these improvements in dropout rates, in graduation rates, if we just watched or observed or really didn’t do anything about it.

What does this all mean? Well, maybe nothing at all. It could simply be one of several threads in a broader conversation about the federal role in K-12, which we know is the crux of Alexander and Murray’s ongoing negotiations.

Or it could be something the White House considers important enough to go to bat for. Either way, we’ll see in the coming weeks when Alexander and Murray unveil the long-awaited results of their ongoing negotiations.

Alyson Klein contributed to this story