Yes, a U.S. federal district or circuit court judge can administer the oath of office to a newly elected member of Congress in such a scenario, though the situation is unusual and context-dependent. The U.S. Constitution (Article VI, Clause 3) requires members of Congress to take an oath to support the Constitution, but it does not specify who must administer it. In practice, the Speaker of the House typically administers the oath to new members during a formal swearing-in ceremony after a special election, as outlined in House Rules and 2 U.S.C. § 25. However, if the Speaker refuses or is unable to perform this duty, there is no constitutional or statutory prohibition against another official, such as a federal judge, administering the oath. The key requirement is that the member-elect has been certified by their state as the winner of the special election, as state certification establishes their legal status as the elected representative (2 U.S.C. § 8). Federal judges, as officers authorized to administer oaths under 5 U.S.C. § 2903, can legally perform this function. Historical precedent supports this flexibility: for example, in rare cases, members-elect have been sworn in by local officials or notaries when circumstances prevented the Speaker from doing so, such as during recesses or emergencies. However, the House retains ultimate authority to determine the qualifications of its members (Article I, Section 5, Clause 1). If the Speaker’s refusal reflects a broader dispute within the House (e.g., over the election’s validity or the member’s qualifications), the House could challenge the member’s seating, regardless of who administers the oath. In such cases, the member might be seated provisionally until the House resolves the matter, as seen in historical disputes like the 1969 case of Powell v. McCormack. In summary, a federal judge can swear in the member-elect if the state has certified their election, but the Speaker’s refusal could signal procedural or political complications that the House would need to resolve. If you need further analysis of specific legal precedents or practical implications, let me know!