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We describe a laser-driven x-ray plasma source designed for ultrafast x-ray absorption spectroscopy. The source is comprised of a 1 kHz, 20 W, femtosecond pulsed infrared laser and a water target. We present the x-ray spectra as a function of laser energy and pulse duration. Additionally, we investigate the plasma temperature and photon flux as we vary the laser energy. We obtain a 75 μm FWHM x-ray spot size, containing ∼106 photons/s, by focusing the produced x-rays with a polycapillary optic. Since the acquisition of x-ray absorption spectra requires the averaging of measurements from >107 laser pulses, we also present data on the source stability, including single pulse measurements of the x-ray yield and the x-ray spectral shape. In single pulse measurements, the x-ray flux has a measured standard deviation of 8%, where the laser pointing is the main cause of variability. Further, we show that the variability in x-ray spectral shape from single pulses is low, thus justifying the combining of x-rays obtained from different laser pulses into a single spectrum. Finally, we show a static x-ray absorption spectrum of a ferrioxalate solution as detected by a microcalorimeter array. Altogether, our results demonstrate that this water-jet based plasma source is a suitable candidate for laboratory-based time-resolved x-ray absorption spectroscopy experiments.