"I would make [the coronavirus vaccine] generally available to them, to the extent possible, while we focus on these prioritized groups," Dr. Scott Gottlieb, member of the boards of Pfizer and biotech company Illumina and former FDA commissioner, told CNBC's "Squawk Box" Monday about the coronavirus vaccine rollout. "I'm not saying ignore that mission. That's a very important public health mission but we shouldn't be spending three weeks trying to push the vaccines into arms where you have some reluctance when we know those vaccines are sitting on the shelf and building on the shelf."