Q:

critical density to create macroscopic nuggets of nuclear matter

Is there a critical size that an hydrogen bomb detonation needs to have in order to produce neutron-degenerated matter?
Does anyone knows if matter in this state would be stable at ambient temperature or pressures? is there any way we can obtain stable "nuggets" of nuclear matter?

A:

According to Wikipedia the pressure inside an atomic explosion maxes out around $10^{15}$Pa. By comparison the pressure in a neutron star is around $10^{34}$Pa. The 19 orders of magnitude difference is too large to be achievable just by making the bomb larger i.e. you will never be able to make neutronium in an atomic bomb.
As Ron explains in his answer, neutronium is unstable under normal conditions. If you extend your definition of degenrate matter to include strange matter then there have been suggestions that this could be stable. However I don't know of anyone who takes the prospect very seriously.

