Hi shubunkin,
Chenepodium berlandieri
Tetragonia tetragonioides
Abelmoschus esculentus
Phaseolus acutifolius
Setaria italica

Collect your spring/summer rain and use it for your garden in the summer.

Most could not go "weeks"--if you mean, a month with no supplemental water at all-- at least, not and do well.
Okra endures drier conditions than many vegetables. Maybe some kinds of beans?
Mulch! Helps reduce water requirements, but not to zero.
Also use graywater? So the answer to your question includes suggested species (you can Google for some other ideas); water conservation; and use of water that is allowed under the law.

AMARANTH king of the cereal grains. Complete protein and one of only three grains to have all the amino acids.(quinoa and spelt being the other two) the leaves are edible as well as the seeds. Some varieties were breed for tastier leaves some for, abundant seeds, some are in between.
You might also consider ordering seeds already adapted to drier climates. nativeseeds.org is a company devoted to preserving the veggies seeds of the tribes from the southwest. And of course collecting the rain off your roof as others suggested, would work great, if you have place to keep it in the meantime.

Lima beans are considered somewhat drought & heat tolerant, tho I noticed that mine have some spider mite 9a bad problem for me in drought years). The variety I have is Fordhook 242.