Check IACV, behind the intake manifold. On both my Integra (b18b) and the CRX (Dohc ZC), I had idle problems, and problems with cold starts. I took off the IACV and cleaned it out with brake cleaner, reassembled, now they both run fine.

There could also be a couple of other issues, but these are the cheapest and easiest to try.

I'm almost 100% possitive it is not your fuel pump. It is rare that honda fuel pumps fail in the fact that they are not effiecent enough to pump enough gas, they usually just straight break. And this sounds more like an emission equipment related problem.

Hope this helps.