John,
A quick google search indicates the primary blooming season is late spring, like May and early June. Sounds like about a three-week peak blooming period. There is some time connection with the blooming following the winter rains. I did the search subject as "desert cactus flowers," so you can follow up.
That would be a beautiful time to go there! We were at Arches National Park in Utah one time in the spring when the cacti were just starting to bloom.
