SJSU, like all CSUs, has fairly extensive GE requirements: http://info.sjsu.edu/web-dbgen/narr/static/schedules/general.html
However, I am not aware of the general level of rigor, though (like most schools, including most more selective schools) it is likely that there are high and low rigor options in most or all of the categories (e.g. physics for physics majors versus physics for poets – compare the “intensive science and math” lists to the other lists of science and math GE course lists).
You can get an idea of what SJSU’s admission thresholds for different majors have been at http://info.sjsu.edu/static/admission/impaction.html .