  At nanohertz frequencies gravitational waves (GWs) cause variations in
time-of-arrival of pulsar signals potentially measurable via precision timing
observations. Here we compute very-low-frequency GW sensitivity constrained by
instrumental, propagation, and other noises fundamentally limiting pulsar
timing observations. Reaching expected GW signal strengths will require
estimation and removal of $\simeq$99% of time-of-arrival fluctuations caused by
typical interstellar plasma turbulence and a reduction of white rms timing
noise to $\sim$100 nsec or less. If these were achieved, single-pulsar
signal-to-noise ratio (SNR) = 1 sensitivity is then limited by the best current
terrestrial time standards at $h_{rms} \sim$2 $\times 10^{-16}$ [f/(1
cycle/year)]$^{-1/2}$ for $f < 3 \times 10^{-8}$ Hz, where f is Fourier
frequency and a bandwidth of 1 cycle/(10 years) is assumed. This sensitivity
envelope may be optimistic in that it assumes negligible intrinsic pulsar
rotational noise, perfect time transfer from time standard to observatory, and
stable pulse profiles. Nonetheless it can be compared to predicted signal
levels for a broadband astrophysical GW background from supermassive black hole
binaries. Such a background is comparable to timekeeping-noise only for
frequencies lower than about 1 cycle/(10 years), indicating that reliable
detections will require substantial improvements in signal-to-noise ratio
through pulsar array signal processing.
