[throwaway_law]

Like all things in physics on its face its easily acceptable, but when you think about the concept looking at a particle closer up when that particle takes up no space (I think saying infinitely small is wrong) its hard to wrap the mind around.

[Filligree]

Particules absolutely take up space, but there are multiple incompatible senses of 'space' you might mean, none of which quite match with intuition.

The closest thing to a "physical size" is probably the typical size of the wavefunction when arranged in typical fashion as part of solid matter, but then you have to specify a cutoff point -- "90% of the wavefunction is in this volume", as 100% would be infinite -- as well as the 'typical fashion'. Free electrons have far less compact wave-functions than bound ones.

The property that affects things-which-we-would-think-are-affected-by-physical-size most is the scattering cross-section, however, which is a completely different concept.