I actually consider the discovery issue, revealing the tax returns, to be the big issue here. The claim of “absolute immunity” is more a media creation/extension of Trump’s arguments than a real legal doctrine.
There is a potent legal issue that I would love a ruling on: the patent absurdity of the DOJ’s “cannot indict a sitting a President” rule, but that issue is not before the Court in this case (or in any of the cases currently pending; the biggest single reason that terrible DOJ rule is still in place is that due to the structure of our system, there’s no way to actually get that question into federal court unless a state prosecutor tried to indict the President.)
Instead, the Trump team have argued that based on that policy that the DOJ shall refrain from indicting the sitting President, that somehow is equivalent to immunity (it is functionally equivalent to a degree, but not at all legally equivalent), and then on top of that, the Trump team argues this immunity is so vast it precludes any investigation of the President at all. That claim is likely to be litigated in the current case and that is where the action is.
It’s kind of funny, given how right wing judicial theorists have screamed about the Court in the 60s extending the right to privacy in the Griswold case and others using a “Penumbra” theory (there is no right to privacy expressly by name in the Constitution but the Griswold court inferred that right from other text and principles of the Constitution). The right wing has screamed for decades that the Griswold court basically “made up a right”, etc. What’s funny is, this legal theory of Trump’s is way more of a reach than Griswold. This whole absolute immunity crap is some kind of insanely inflated “penumbra” theory derived not from the text of the Constitution and two centuries of American legal history like Griswold, but from DOJ memos prepared by the DOJs of two Presidents who had been investigated or impeached (Nixon and Clinton). It’s an extremely bad theory, legally worthless, lacking in any kind of foundation of precedent, strongly contrasted by numerous other cases that the President is not an absolute sovereign, and also contradicted by the centuries of history and legal precedent on the rule of law, the co-equal branches of government, checks and balances, etc.
It will take a serious reach past any kind of “good faith but legally conservative” view of the law to hold in Trump’s favor. On top of that, there is a serious issue of “dangerous precedent” in that if the USSC immunizes the Presidency like Trump wants, that’s a dog whose bite may be felt on the skin of more than just Trump’s enemies in future decades.
So I want to believe the USSC will not rule for absolute Presidential immunity (the lesser DOJ “immunity” is a separate issue not before the court). However, since we can’t have nice things I only give this a 60% chance. But hey that’s better than 0.