I don't think the articles of the US Constitution were intended to operate sequentially, were they? So if the House is investigating or impeaching him, the President plays golf.
US Constitution Article 1: "All legislative Powers herein granted shall be vested in a Congress of the United States, which shall consist of a Senate and House of Representatives .... The House of Representatives shall choose their Speaker and other Officers; and shall have the sole Power of Impeachment."
US Constitution Article 2: "The executive Power shall be vested in a President of the United States of America.... I do solemnly swear (or affirm) that I will support and defend the Constitution of the United States ... and that I will well and faithfully discharge the duties of the office on which I am about to enter." --- (unredacted version) BUT ONLY IF THE HOUSE IS NOT INVESTIGATING ME!
Holding the entire legislative machinery hostage to ceasing an investigation of the president sounds to me just a teeny weeny bit like obstruction of justice.
At what point will Trump pretend it was just another joke? Such a crack, that Trump. He ought to do standup. Or stand down.