Art. II §3: He shall from time to time give to the Congress information of the state of the union, and recommend to their consideration such measures as he shall judge necessary and expedient; he may, on extraordinary occasions, convene both Houses, or either of them, and in case of disagreement between them, with respect to the time of adjournment, he may adjourn them to such time as he shall think proper; he shall receive ambassadors and other public ministers; he shall take care that the laws be faithfully executed, and shall commission all the officers of the United States.
Pretty much says right there in black and white that be may adjourn congress.
Since the congress is using obscure parliamentary procedures to technically keep itself "in session", in order to prevent the president from appointing needed officers, it might be time to dust that provision off. If congress would like to get back to DC and actually do their jobs, it wouldn't be necessary for him to do so. If he feels the need to execute this power, he could also invite them back whenever they are ready to actually muster a quorum and do their jobs.
OTOH, no one's life, liberty, or property are safe while the legislature is in session.
Either way, the resulting shit-storm would be fun to watch.