The Republican House should sue the DoJ for mandamus. That privilege assertion is unmitigated BS and is also an admission that the WH is directing Garland in what to do or not do.
So, I 'm not sure that can be done by the House either. But since I have no formal training, or even informal training for that matter, I may again be wrong, and would be perfectly happy to be wrong here also.
Conversations by the President when he is talking to a top aide may (e.g. Navarro, Bannon, etc.) be subject of executive privilege and not divulged BUT certainly NOT being interviewed by law enforcement or a prosecutor!! Beam me up!