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.
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.