Some attorney may correct my perception, but there appears to be no legal authority over supreme court recusal. Specifically, both Kagan and Sotomayor could have lost their jobs if the Kerchner case had resulted in the removal of an ineligible Obama. Kagan was solicitor general, working for the executive branch, when a half dozen eligibility cases were appealed to the Supreme Court.
Kagan and Sotomayor refused to recuse themselves from the vote to determine whether the court would hear the Kerchner case. We don't have access to the vote, but there was an announcement that the "rule of nine" resulted in the court's decision not to hear the case. Had Kagan and Sotomayor recused themselves there would have been a "rule of seven", and even Roberts, who seems likely to be one of those protecting Obama, and not the Constitution, couldn't have rejected the case. This probably holds for other cases, including the several Donofrio cases. Any case which could remove their patron, and thus his lifetime appointments are a patent conflict of interest. These justices were voting themselves millions of dollars in benefits by protecting Obama. Grounds for impeachment of justices?
You are right that there is no way to enforce recusal rules as against SCOTUS Justices. (There is some dispute whether Justices, as opposed to lower federal judges, are subject to the recusal STATUTE at all, enforceability aside. So I’m going to focus on the ethical rule: Recuse if your impartiality might reasonably be questioned ... and refrain from public pronouncements about matters reasonably likely to come before your court.)
Kagan surely should have recused herself from the ACA case, for example, and she didn’t. Now I worry that Scalia may fall under the rule later when a new immigration case comes along. Whether or not he recuses himself in fact, I worry — and that is why I would have preferred that he maintained his neutrality, publicly, on any “issue likely to come before the court.” I don’t want us to start saying, “Well, Kagan got away with it, so we can too.”