Where can I find a simple TOWNSHIP/RANGE, SECTION, QUARTER SECTION shapefile for Adams County Colorado?
Goto navigator.blm.gov . This has the PLSS data for many of the States in US
You could try datagateway.nrcs.usda.gov.
The Geospatial Data Gateway (GDG) provides access to a map library of over 100 high resolution vector and raster layers in the Geospatial Data Warehouse. It is the One Stop Source for environmental and natural resources data, at any time, from anywhere, to anyone. It allows you to choose your area of interest, browse and select data, customize the format, then review and download.
Also, you can try an alternative the direct download as well - Public Land Survey System of the United States - Direct Download