  Using high temperature expansions for the equal time correlator $S(q)$ and
static susceptibility $\chi(q)$ for the t-J model, we present evidence for
quantum critical (QC), $z\!=\!1$, behavior at intermediate temperatures in a
broad range of $t/J$ ratio, doping, and temperatures. We find that the
dynamical susceptibility is very close to the universal scaling function
computable for the asymptotic QC regime, and that the dominant energy scale is
temperature. Our results are in excellent agreement with measurements of the
spin-echo decay rate, $1/T_{\rm 2G}$, in La$_2$CuO$_4$, and provide qualitative
understanding of both $1/T_1$ and $1/T_{\rm 2G}$ nuclear relaxation rates in
doped cuprates.
