A large increase in quiet network area since the 17th century Maunder Minimum has been suggested as a mechanism for increasing solar irradiance sufficiently to drive global warming. We show that this mechanism requires essentially complete disappearance of network proceeding back in time to the beginning of the 20th century. This disappearance is ruled out by the many Ca K spectroheliograms taken since the discovery of the network in the early 1890's. Furthermore, network area measurements we have carried out on Ca K spectroheliograms digitized from the Mt. Wilson and NSO/Sacramento Peak archives, for the nine solar activity minima between 1914 and 1996, show no evidence of network area variations large enough to produce a significant long-term component of total irradiance variation. A network brightness variation of sufficient magnitude is also unlikely, given the linear dependence of solar microwave flux on area of bright structures. More generally, recent analyses of cycle 21, 22 pyrheliometry, and of broadband stellar photometry, provide little support for any long-term irradiance component. These results do not rule out a secular irradiance increase. But they suggest that high climate sensitivity to the relatively small changes in solar total and UV irradiance that have been observed, provides a more likely explanation of the global temperature-solar activity correlation. ¿ 2001 American Geophysical Union