As far as I understand it the US cabinet is nominated by the president, but the senate has to consent to the nominees. The same applies applies to judges of the Supreme Court.
But what happens if the senate does not give consent to a candidate? Would it in the case of the cabinet be an interim cabinet until a candidate is accepted by the senate? Or will there be a vacancy in the cabinet? Is there a risk that there are issues that will need to be taken care of while there's nobody in office?
The same question applies for the Supreme Court, but I assume that normally there would be enough judges to be able to carry out it's obligations even if one judge is missing.