“And I saw this early on, and I've seen proof of it, where they have a vaccination thing, looks like the size of a bottle of soda, poured into a little child's body.”

Oval Office remarks on signing the childhood vaccine executive order

A childhood vaccine dose is half a millilitre. The CDC's vaccine administration table gives the standard dose of DTaP, MMR and varicella as 0.5 millilitres each, with 1.0 millilitre reserved for certain adult formulations. Half a millilitre is about a tenth of a teaspoon, and nothing on the childhood schedule is given in a larger volume than the one millilitre reserved for those adult formulations.

Several vaccines can be given at one visit, and that is the claim's best defence. CDC guidance provides that if multiple vaccines are administered at a single visit, each preparation goes at a different anatomic site. Each remains a small dose, and no combination at any visit approaches the volume he described.