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.

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