Sure the SC is there to consider the legal question but you can not ignore that the notion of causing an actual major economic crisis by putting a stay in place while they spend weeks/months on the case would weigh heavily on their mind.
A stay is one thing if your talking about temporary inconvenience but as has been said, you don't just undo a default. The irreparable damage of a stay, and therefor forced default, compared to just punting the debt ceiling forward until they give a verdict would, to my laymen mind, make it completely unreasonable to issue a stay.