Washington CNN  — 

The Roger Stone aide who is mounting a constitutional challenge to special counsel Robert Mueller wants to take his case to the Supreme Court and feels “great” that Justice Brett Kavanaugh will be on the bench to, hopefully, deal a major blow to the Russia investigation.

Andrew Miller previously worked as an aide to Stone, a longtime Trump ally who is under scrutiny in the Russia investigation. Miller was subpoenaed earlier this year to testify before the special counsel’s grand jury. Instead of complying, he waged a legal battle to invalidate Mueller’s authority to act as a prosecutor. A federal judge ruled against him, holding him in contempt of court for failing to testify, and he has appealed to the US Court of Appeals for the District of Columbia Circuit

Asked how he feels about Kavanaugh’s presence on the court, as someone who might be sympathetic to his case, Miller said, “I feel nothing but great. I’m cool as a cucumber now.”

Miller made the comments on a radio show Tuesday morning, when Kavanaugh heard his first oral arguments as a newly minted justice. The program on WBEN in Buffalo, New York, was hosted by former Trump campaign aide Michael Caputo, a staunch Mueller critic who has been questioned as part of the investigation and is partially funding Miller’s legal team.

Earlier in the show, Miller’s attorney said he hoped to take the case to the Supreme Court and predicted that a majority of the justices would support his argument against Mueller’s authority, if they decided to take the case. The probability that Kavanaugh and his colleagues on the court would get to hear Miller’s challenge of Mueller anytime soon is a stretch.

For the case to reach the Supreme Court, Miller would have to lose at the appellate court first. His case is scheduled to be heard by three appellate judges on November 8, and a decision would come later.

Kavanaugh would be “very good on this issue,” Miller’s attorney Paul Kamenar said on WBEN.

“He would be a good ally,” Kamenar said of Kavanaugh, “because he has talked about these cases before in terms of presidential power and limiting the power of the government and has written about this very issue of the constitutionality of the independent counsel.”

Kavanaugh previously worked for independent counsel Ken Starr, whose investigation of President Bill Clinton in the 1990s led to Clinton’s impeachment. But years later, Kavanaugh shifted his views and struck a much more hostile tone against independent prosecutors.

While Mueller is frequently compared to Starr in day-to-day discussions, the law Kavanaugh has weighed in on governed a prosecutor who could exist outside the three branches of the federal government, like Starr did. Mueller operates much differently than Starr, because his office works within the Department of Justice and he reports to the attorney general.

So far, four federal judges – including the one who ruled on Miller’s case at the trial court level – have upheld Mueller’s appointment and authority to bring the cases he prosecuted. Two of the judges were appointed by Democrats and two were tapped by Republicans, including one by President Donald Trump.

While Miller and Trump have a shared goal of opposing Mueller, they don’t have much else in common. Miller worked for Stone, a staunch Trump supporter, during the presidential campaign but they parted ways over Trump, because Miller said he expected that Trump “would leave us high and dry.”

“I’ve never meshed well with his personality,” Miller said on Tuesday’s radio show. “I don’t really like that bulldog way.”

A self-identified Libertarian, Miller mentioned how he had sneaked the Libertarian presidential nominee Gary Johnson into the 2016 Republican National Convention to do TV interviews.

“I just don’t believe in political parties,” Miller said. “Parties crush our political system.”

Miller worked for Stone on and off as a traveling aide, driver and tech guy who handled Stone’s website. Stone-linked political groups paid Miller’s company $14,000 during the 2016 election cycle, according to federal records. He is one of a handful of Stone associates who were interviewed by investigators this year or gave testimony to Mueller’s grand jury. Miller talked for two hours with FBI agents at his Missouri home earlier this year.

Stone styles himself as a political dirty trickster who pushes the limits. But he is adamant that he is not a traitor and would never work with a foreign government to influence US elections.

Miller’s lawyers say he had no contact with Russia or WikiLeaks during the 2016 campaign. His comments Tuesday were the first time he has spoken publicly since his case got national attention in June.

CNN’s Katelyn Polantz contributed to this article.