I've got 512mb and had 300mb free at the time of the first attempt. The second attempt the files were all on a HD partition, so RAM was not an issue. I watched it closely and never came close to running out.
I've given up on ezremaster and have been doing it manually, which is taking a lot of trial and error, but is working. My extracted base initrd with the extensions extracted into the file system is under 15mb before compression with gzip and advdef. Which tells me there is something seriously broken in ezremaster because it was somehow coming up with a 300mb tinycore.gz after the gzip process.
The whole point of me remastering it is for speed of booting, I don't want to have to wait for it to extract my wireless stuff, window manager and a few other basic essentials every time it boots. So anything but extracting them into the filesystem is not an option.
Right now I have a 13mb initrd which includes the microcore with Xvesa, fluxbox, wireless_tools, wpa-supplicant, wireless modules, OSS, 915resolution and acpi. A similar set of packages caused ezremaster to leave me with a 250mb initrd.