I'm pretty sure you can find MIPS Linux images with Busybox et. all. that weigh less than that. A lot of routers run Linux on 2M eproms including user space.
For those who don't know who Alan Cox is, he was the Linux 2.2 branch maintainer, is still heavily involved in Linux, and also does lots of other neat shit.
I used to have a 1.44Mb floppy that booted QNX to a desktop environment. Of course, that's not so unusual historically: both Amiga and GEM had single-floppy desktop enviroments (or did the Amiga require two to get to Workbench?)
You won't find anything remotely recent squeezing into a mere 2MB. You can't really get Linux that slim anymore without cutting out major things like the network stack. 4MB is still (just barely) enough ROM for a real router, if you're judicious about what features to include, and don't mind the lack of a browser-based configuration interface.
(That's actually quite big for a tiny-computer OS, although it's the smallest Unix I know of.)