If the House REALLY wants to press the contempt issue...
There is the "inherent contempt" power, where the House orders the arrest of the defendant, and can try him then and there, and pass sentence. It hasn't been used since 1934, when the Senate sentenced a fellow who destroyed evidence to ten days in jail. It was upheld by the Supreme Court in Jurney v. MacCracken, 294 U.S. 125 (1935). ("Here, we are concerned, not with an extension of congressional privilege, but with vindication of the established and essential privilege of requiring the production of evidence. For this purpose, the power to punish for a past contempt is an appropriate means.") The House sends out its Sergeant-at-Arms to arrest the defendant, he is tried on the spot, and the House decides whether to convict.
All the more ironic, in that not too many years ago the Demos were suggesting its use against a Republican administration. One pointed out that the the Capitol has an unused jail cell for just that occasion.
Hat tip to Jim Norell, a husband of the late Nancy Norell and a former Senate staffer who reminded me of the Capitol "dungeon."