  The antiferromagnetic spin correlation function $S_{\bf Q}$, the staggered
spin susceptibility $\chi_{\bf Q}$ and the energy scale $\omega_{FL}=S_{\bf
Q}/\chi_{\bf Q}$ are studied numerically within the t-J model and the Hubbard
model, as relevant to cuprates. It is shown that $\omega_{FL}$, related to the
onset of the non-Fermi-liquid spin response at $T>\omega_{FL}$, is very low in
the regime below the 'optimum' hole doping $c_h < c_h^* \sim 0.16$, while it
shows a steep increase in the overdoped regime. A quantitative analysis of NMR
spin-spin relaxation-rate $1/T_{2G}$ for various cuprates reveals a similar
behavior, indicating on a sharp, but continuous, crossover between a
Fermi-liquid and a non-Fermi-liquid behavior as a function of doping.
