This, and other stories in the media like it makes me wonder if a possible strategy for Trump would be to find a judge that would order the Democrat committees and House to immediately halt proceedings that violate the President's constitutional rights. The order could read: "The committees are to cease and desist all votes that are taken in violation of these rights, and any such votes that are taken in violation of this order are declared null and void".
This would then tie up any impeachment activities until there is a Supreme Court ruling, which would likely be so close to the election that it would become moot.