That is NOT how it works. The House has NO AUTHORITY to demand anything on Impeachment from the President or the executive Branch UNLESS they voted for impeachment. YOU know it I know it and so do the Congress and the White House.So... the White House says they will not cooperate until there is a vote on impeachment, just so they can say that there was a vote for impeachment without a proper investigation. Just how dumb is Trump and his lackeys?
White House, State Department, and other staff will be asked to testify, if they refuse they will receive a subpoena. If Trump tells them they are not allowed, he will then be openly committing obstruction and there will be no need for an investigation. End of story.
It doesn't take a whole lot of intelligence to see the road map here.