Well in this case the executive branch isn't even following congressionally appropriations, so one could argue that this particular shut down is more caused by the president than any other in history.
AFAIK this kind of situation is a result of a novel interpretation by an AG of a much older law some time around 1980. I don't think it's ever been tested in court, and we'd operated for decades under the old interpretation before then.
Trump could just say "we're going back to the old interpretation" and at-minimum buy several months of runway while court challenges happened (if they even did). This would be among the least questionable "stretches" (to be very generous) of presidential power he'd exercised.
