This is mostly enhancing Nik Weaver's comments.  Suppose  that $M$ is compact of dimension $m$. For a generic metric $g$ on $M$ the eigenvalues $\lambda_k$  of the Laplacian $\Delta_g$ are   simple.  Weyl's spectral estimates then imply that

$$\lambda_k \sim C_m k^{\frac{2}{m}},  $$

where $C_m$ is an explicit universal constant that depends only on $m$. In particluar this shows that for $m\geq 2$ and a generic metric  we have

$$\lambda_{k+1}-\lambda_k =O(1). $$

Now Nik Weaver's argument shows that there exists $r_0>0$ such   for any $\xi\in [0,\infty)\setminus {\rm spec}\;(\Delta)$  we have  $\Vert(R(\xi)\Vert\geq r_0$.