He is thinking about a compactification of M-theory on G2-holonomy manifolds and/or various type II string theories with a large number of axions. The potential for these axions is generated from D-brane instantons, and if the action of the instanton is around 210-290, Peter argues that you obtain more or less the observed value of the cosmological constant.
Yes, the number is the exponent from Polchinski's new favorite form of the cosmological constant written as a multiple of "M_{Planck}^4".
As far as I understand, Peter still does not explain why the remaining contributions to the vacuum energy cancel, but if they cancel, he could eliminate one of the "new cosmological constant problems" that appeared when a nonzero value was measured.
I was just thinking about a framework to imagine that the SUSY breaking is mathematically analogous to the chiral symmetry breaking: in the latter case, small bare quark masses break the chiral symmetry and imply a vev of quark bilinears that is much larger - at a scale somewhere in between the bare masses and the QCD scale.
In a similar way, small bare masses in the milli-eV range could create vevs around a TeV that split the supermultiplets, but the vacuum energy could still be dictated by the small bare masses.
