Since there are no takers for my previous question ("what exactly is the constitutional issue here?"), I'll offer my opinion:
There is no constitutional issue here, short of providing for the possibility of impeachment and providing a procedural framework for it.
It is, by design, a political act.
The constitution doesn't not define what "high crimes and misdemeanors, etc." are. No need for a crime either. If a president gives someone the evil eye, they can impeach him for that.
So, defining what happen re Ukraine as a bribery is a political act. Claiming it endangered national security is a political act. Everything regarding impeachment is a political act, not judicial, nor constitutional (except for what I mentioned above).
I wouldn't go that far. There are limits in the constitution that refer to actual crimes. The exact words in the Consitution are as follows:
SECTION 4. The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors.
There has to be some nexus to an actual crime. Treason and Bribery are real crimes. While the House can certainly impeach for political reasons, and interpret high crimes and misdemeanors however they want, Americans won;t stand for it. After all, a little less than half the country voted for the president. They know a crime or not and they know a political act or not.
Americans want to vote their presidents in or out of office during an election. Otherwise, we'd have impeachments every time Congress was held by the opposite party. That would be terrible for government and the country. The bickering is preventing real work from getting done. The public realizes this. That's why they won;t stand for political impeachments.