  We study dynamics near the threshold for blowup in the focusing nonlinear
Klein-Gordon equation $u_{tt}-u_{xx} + u - |u|^{2\alpha} u =0$ on the line.
Using mixed numerical and analytical methods we find that solutions starting
from even initial data, fine-tuned to the threshold, are trapped by the static
solution $S$ for intermediate times. The details of trapping are shown to
depend on the power $\alpha$, namely, we observe fast convergence to $S$ for
$\alpha>1$, slow convergence for $\alpha=1$, and very slow (if any) convergence
for $0<\alpha<1$. Our findings are complementary with respect to the recent
rigorous analysis of the same problem (for $\alpha>2$) by Krieger, Nakanishi,
and Schlag \cite{kns}.
