We set forth a conceptual design for an X-ray all-sky monitor based on lobster-eye wide-field telescopes. This instrument, suitable for a small satellite, would monitor the flux of objects as faint as 2x10^-12 erg cm^-2 s^-1 (0.5-2.4 keV) on a daily basis with a signal-to-noise ratio of 5. Sources would be located to 1-2 arcmin. Detailed simulations show that cross-talk from the cruciform lobster images would not significantly compromise performance. At this sensitivity limit, we could monitor not just X-ray binaries, but also fainter classes of X-ray sources. Hundreds of active galactic nuclei, coronal sources and cataclysmic variables could be tracked on a daily basis. Large numbers of fast transients should be visible, including gamma-ray bursts and the soft X-ray breakout of nearby Type II supernovae.