A basic question is: How much water to carry? If you hike in fall, winter or spring it's: 3-4 liters/day for each hiker for drinking purposes in the north Dan to Arad, and 5-6 liters/day for each hiker for drinikng from Arad to Eilat. The month of May in Israel for all practical matters is summer, not spring.
If you decide to hike during summer time (May/June to August), well, it is not recommended at all. If you still hike in summer, then more water is required up to 8-9 liters/day may be required for each hiker in the south.
During summer at day time tempertures are really hot 35-45 C / 95-115F and only on the mediterranean shore is a little cooler 29-32C / 85-90F but with 65-75% relative humidity. It takes 3-4 minutes to fry and egg in the desert, using an aluminum plate or just a rock...I mean without any fire...
If you plan properly you need to carry water only for one day. Naturally you'll need to arrange for water drops (caches) before you start the desert section.
It is not recommended to carry water for two days, it's too heavy.
How to arrange a water drop? There are people in the Negev desert who'll take you on a 1 day tour for all water drops in the desert (12 of them).
Share a ride is almost always available. Such a trip costs approx. 1500 shekels (aprox. $400) but if you consider that the ride is shared by 3-4 groups
it means $100-130 for your group for all 12 caches. Usually only one hiker from each group takes the caching trip.