I spoke too loosely here. What I mean to say is that, even if the First Amendment didn’t exist, the President must obviously be immune from any restriction on a

I spoke too loosely here. What I mean to say is that, even if the First Amendment didn’t exist, the President must obviously be immune from any restriction on any of his speech that would be even a barely plausible basis for making policy, persuading voters and other elected officials, exercising his authority over the executive branch (especially the parts closest to him), wielding the country’s international leverage. His immunity probably cuts into some areas currently prohibited despite the First Amendment as well, like obscenity, some kinds of financial crimes (e.g. improper disclosures about public companies), workplace harassment, discrimination in hiring and managing the White House Office and cabinet, etc. He can of course be impeached for any of those things. The President can be impeached for any reason. The only real requirement is that 1/2 of the House and 2/3 of the Senate agree to it. They are the only and final arbiters of impeachment.