(CNN) As President Donald Trump's legal team continued its will-he-or-won't-he dance this week on a sit-down interview with special counsel Robert Mueller, a federal judge in Washington issued a tome on why Mueller's appointment was rock-solid in the first place.

Chief Judge Beryl Howell's decision is not entirely novel; it falls in line with two other district court judges in DC and Virginia who have rejected challenges to Mueller's appointment. But her robust analysis guts a potential avenue for Trump's defense team at a critical time, as the President calls for the probe to end , his lawyers continue to negotiate over the scope of an interview, and speculation mounts about whether Mueller will ultimately serve Trump with a subpoena to testify.

Legal experts say that while Trump's legal team still has other arguments to make on why he should not have to sit down with the special counsel, the door on challenging Mueller's legitimacy appears to be nearly closed.

What does the opinion say?

Over the course of 92 pages, Howell resoundingly rejected an attempt by Andrew Miller, a former associate of Trump confidante Roger Stone, to quash a subpoena to testify, explaining why the "scope of the Special Counsel's power falls well within the boundaries the Constitution permits."

Miller had argued that Mueller was not nominated by the President and confirmed by the Senate and therefore was unconstitutionally appointed as a "principal officer." Howell found the claim unpersuasive in light of the Supreme Court's decision in Morrison v. Olson, which upheld the constitutionality of provisions of a now-defunct federal statute creating an independent counsel, and subsequent court decisions. Instead, Howell found Mueller to be an "inferior officer" under the supervision of deputy attorney general Rod Rosenstein, who took up the oversight of the Russia investigation after Attorney General Jeff Sessions recused himself from it last year.

"His appointment, without presidential appointment and senatorial confirmation, thus did not violate the Appointments Clause," Howell wrote.

Miller also claimed that Sessions' "mere recusal" from the Russia investigation didn't make Rosenstein the acting attorney general for purposes of tapping Mueller to lead the probe. But Howell didn't buy that argument either, pointing to the fact that various federal statutes allow the attorney general to delegate the authority to appoint a special counsel to the deputy attorney general.

"Multiple statutes authorize the Special Counsel's appointment, and the official who appointed the Special Counsel had power to do so," Howell concluded, underscoring a point previously acknowledged by several prominent legal voices.

"there is no serious argument that Special Counsel Mueller's appointment violates the Appointments Clause specifically or the separation of powers generally." George Conway, the husband of White House counselor Kellyanne Conway, similarly wrote last month, "there is no serious argument that Special Counsel Mueller's appointment violates the Appointments Clause specifically or the separation of powers generally."

And even Supreme Court nominee Brett Kavanaugh has privately told senators that he believes Mueller's appointment was legitimate, though he did not disclose how he would rule on a presidential subpoena.

Why does this matter for Trump's defense?

The President has railed against Mueller's appointment since day one -- but his tirades on Twitter have gone into overdrive in recent weeks.

In early June, he proclaimed: "The appointment of the Special Counsel is totally UNCONSTITUTIONAL!"

The appointment of the Special Counsel is totally UNCONSTITUTIONAL! Despite that, we play the game because I, unlike the Democrats, have done nothing wrong! — Donald J. Trump (@realDonaldTrump) June 4, 2018

More recently, he's asserted, without evidence, that Mueller, a registered Republican is " totally conflicted ," including an alleged "contentious business relationship" between him and Mueller involving a dispute over fees at the Trump National Golf Club in Sterling, Virginia. A spokesman for Mueller told The Washington Post last month that there was no dispute when Mueller, who was then FBI director, left the club in late 2011.

After Mueller's appointment by Rosenstein, a Trump appointee, the Department of Justice determined there was no ethics conflict for Mueller in the investigation.

If Mueller cannot reach an agreement with Trump's lawyers for a voluntary interview with the President, then a grand jury subpoena to force Trump to talk would almost certainly trigger fierce resistance from his defense team.

But some legal experts say Howell's decision casts significant doubt on any effort to successfully challenge the legality of Mueller's appointment.

"Judge Howell's comprehensive opinion denying the challenge to the special counsel regulation is no surprise. Republicans and Democrats alike for two decades have said the same -- the argument to the contrary is well out of the constitutional mainstream," said Neal Katyal, who served as acting solicitor general in the Obama administration and helped draft the special counsel regulations in the 1990s.

"President Trump can try other arguments in the months to come, but this one is going nowhere," Katyal added.

Trump's lawyers have already asserted that a sitting president cannot be subpoenaed, but that's an unsettled legal issue, and it is unclear whether a court would agree.

"Trump can try to argue that presidents are not amenable to subpoena under our Constitution, and that even if they are, the subpoena must be very narrow in scope," Katyal said. "Those are difficult arguments to make, but not impossible ones."