  We present a theory for the large suppression of the superfluid-density,
$\rho_s$, in BaFe$_2$(As$_{1-x}$P$_x$)$_2$ in the vicinity of a putative
spin-density wave quantum critical point at a P-doping, $x=x_{c}$. We argue
that the transition becomes weakly first-order in the vicinity of $x_{c}$, and
disorder induces puddles of superconducting and antiferromagnetic regions at
short length-scales; thus the system becomes an electronic micro-emulsion. We
propose that frustrated Josephson couplings between the superconducting grains
suppress $\rho_s$. In addition, the presence of `normal' quasiparticles at the
interface of the frustrated Josephson junctions will give rise to a highly
non-trivial feature in the low frequency response in a narrow vicinity around
$x_c$. We propose a number of experiments to test our theory.
