In this paper, we study an analogue of size-Ramsey numbers for vertex colorings. For a given number of colors r and a graph G the vertex size-Ramsey number of G, denoted by Rˆv(G,r), is the least number of edges in a graph H with the property that any r-coloring of the vertices of H yields a monochromatic copy of G. We observe that Ωr(Δn)=Rˆv(G,r)=Or(n2) for any G of order n and maximum degree Δ, and prove that for some graphs these bounds are tight. On the other hand, we show that even 3-regular graphs can have nonlinear vertex size-Ramsey numbers. Finally, we prove that Rˆv(T,r)=Or(Δ2n) for any tree of order n and maximum degree Δ, which is only off by a factor of Δ from the best possible.