The solar photon output from the Sun was once thought to be constant but is now known to vary considerably over timescales from seconds during solar flares to years due to the solar cycle. This is especially true in the wavelengths shorter than 208 nm (Al ionization edge), where measurements and models of the solar irradiance at these short wavelengths are needed. The time-variant solar irradiance drives physical changes in the Earth's atmosphere that can affect many things including GPS accuracy and satellite drag rates. The Flare Irradiance Spectral Model (FISM) is an empirical model that estimates the solar irradiance at wavelengths from 0.1 to 190 nm at 1 nm resolution with a time cadence of 60 s. This is a high enough temporal resolution to model variations due to solar flares, where few accurate measurements at these wavelengths exist, as well as the solar cycle and solar rotation variations. The modeling of the FISM daily component, including the solar irradiance variations due to the solar cycle and the solar rotation, is the topic of this paper. The daily component algorithms are given, and results and comparisons of the daily component demonstrate that the FISM estimations agree within the stated uncertainties to the various measurements of the solar VUV irradiance. A third type of event that causes sudden changes in the solar irradiance is solar flares. The FISM modeling of the variations in the solar irradiance due to solar flares is the topic of the second paper.