The White House's fierce response to the impeachment inquiry by the House of Representatives, calling the enterprise "an unconstitutional effort" and a violation of "constitutionally mandated due process," seems to make one commitment: noncooperation.
The key sentence in the eight-page letter, signed by White House counsel Pat A. Cipollone, is this: "Given that your inquiry lacks any legitimate constitutional foundation, any pretense of fairness, or even the most elementary due process protections, the Executive Branch cannot be expected to participate in it."
What can the House do in response?
Let us step back a bit. No White House welcomes a congressional investigation, and an impeachment inquiry is the least welcome of all. Any White House counsel has a duty to protect the president and the presidency (and, if necessary, to do so fiercely). Under both Democratic and Republican presidents, congressional investigations, including scandal-mongering, are often efforts to score political points by obtaining internal documents that may well be protected by executive privilege (which safeguards the confidentiality of presidential conversations).
So the White House's reluctance to hand over documents is hardly unusual. What is unusual is the sweeping vow of noncooperation and this wild objection: "you have denied the President the right to cross-examine witnesses, to call witnesses, to receive transcripts of testimony, to have access to evidence, to have counsel present, and many other basic rights guaranteed to all Americans."
An impeachment inquiry is hardly a criminal trial. In fact, it is not a trial of any kind. In a congressional hearing, whether open or closed, members of Congress typically call witnesses and ask them questions. There is no cross-examination. Does the White House counsel really want the president of the United States or his lawyers to be able to cross-examine and call witnesses? What does that even mean?
Does the White House counsel think that the U.S. Constitution guarantees that right, in the context of an impeachment inquiry?
The House has already issued a subpoena, specifically focusing on the White House's interactions with Ukraine. Compliance with a lawful congressional subpoena is not optional. The House can go to court and attempt to get the subpoena enforced. Alternatively, it can hold the recipient in contempt of Congress (that's a misdemeanor, with a jail sentence).