Michael Cohen has advertised his eagerness to be pardoned using just about every method short of flying a skywriting plane over the White House. This weekend, Donald Trump’s longtime personal attorney and fixer sent the message again, later aired on national television, telling George Stephanopoulos that if he’s forced to choose between protecting the president or spilling what he knows and protecting his family, “My wife, my daughter, and my son have my first loyalty and always will.”

The federal prosecutors in the Southern District of New York were likely unamused by his chattiness. The S.D.N.Y. has been investigating Cohen for months, with F.B.I. agents raiding his Midtown Manhattan office and seizing thousands of documents and 16 cell phones. “If I’m the prosecutor on the case, I’m appalled by all the talking Cohen is doing,” says Bennett Capers, a former S.D.N.Y. prosecutor. “Because every time he opens his mouth, it makes the case a little bit harder. Every time he speaks he jeopardizes his usefulness down the line as a witness, because he might say something contradictory.”

Renato Mariotti, a former federal prosecutor in Chicago, has seen defense lawyers exploit smaller holes than the ones Cohen is gabbing open. “If he gets on the witness stand, he’s going to get impeached on the prior statements: ‘Now you’re saying that Trump was involved in the Stormy Daniels thing. But you said the opposite on this TV show.’ Yeah, that’s gonna be a problem.”

Yet Cohen’s public appeals to Trump, annoying and legally unhelpful as they may be, are unlikely to change the way the S.D.N.Y. is playing its side of this game. Prosecutors likely see no point in dialing up the pressure on Cohen to cooperate, or in rushing to indict him, because a pardon is out of their control and could arrive at any time. “These are professional, career prosecutors. They’ll try to ignore the noise, just as they would in any case that attracts public attention,” a recent S.D.N.Y. alumnus says. “But it’s got to be really tough. They’re human, and it’s hard not to be shaken a bit by the idea that justice could be undermined by something so blatantly political. Prosecutors know one thing: how to investigate cases, and they trust that there’s a system and everyone plays by the rules. What’s happening with Cohen right now is all outside that process.”

So the S.D.N.Y. is quietly going about its business, assembling evidence, content to let Cohen twist in the wind. It is expected that the prosecutors will soon reach out to Cohen’s new defense lawyer, Guy Petrillo, and reiterate the S.D.N.Y.’s willingness to listen to whatever his client has to say, but that’s a formality: Petrillo spent nearly 10 years as an S.D.N.Y. prosecutor. “Guy is a great lawyer. The full package,” says Dan Stein, former chief of the S.D.N.Y.’s criminal division, who took on the role a few years after Petrillo left. “The idea that because he’s a former chief of the criminal division he’s just going to cut a deal and roll the guy over is not accurate. After Guy became a defense lawyer he was representing a client we very much wanted to flip in a public corruption case, and Guy called our bluff and prevailed. His client was not charged.”

All the focus on what Cohen might do has obscured another key part of the maneuvering. “When all the pundits talk about whether Cohen is going to flip, people leave out the other half of that equation—which is that the Southern District has to want to offer him a deal. It’s not clear to me they would,” says Stein, who left the office in November 2016. “Typically you only want to sign someone up as a cooperator if there’s a reasonable prospect of using them in a case against a bigger target. Here, where the target appears to be the president, who is potentially immune from prosecution, where are you going to have Cohen testify? My instinct is the Southern District would be uncomfortable with making a deal with Cohen and then just saying to Robert Mueller, ‘Here are the proffer notes, do with them as you will.’”

Perhaps; the S.D.N.Y. is indeed famous, or infamous, for being protective of its cases. But proffers and plea deals are sometimes shared by jurisdictions. “True, the Southern District is not going to prosecute Trump for Russian collusion, because that’s the special counsel’s turf,” says Mimi Rocah, another former S.D.N.Y. prosecutor. “But there are certainly a world of crimes that Southern could investigate and prosecute apart from Mueller—say, if Cohen has information about fraud or real-estate crimes before Trump was a candidate. It takes close coordination to share what a cooperating witness proffers, but if there’s a dynamic where it would happen, this would seem to be it—given that what’s at stake is the criminality or non-criminality of the president of the United States.”