A healthy, reasonably fit person can cover about 5km per hour, with an additional 1 minute for every 10 metres of altitude gained (Naismith's rule). Considering that area of the desert is seemingly quite flat, in ideal conditions, 24km should be coverable in about 5 hours. Of course heat would affect this estimate considerably, therefore travelling in the cooler parts of the day would be highly recommended.
The bigger issue here is water, or lack thereof, and 30 hours without would put a serious dent in anyone's ability to move more than a few hundred metres. In this case they had a unique advantage though - a mobile lab at their disposal. Windscreen washer systems contain a reasonable amount of water, and older vehicles (such as the 1986 Fleetwood Bounder depicted in the show) often use water in the radiator system. If that was the case, they could have distilled much of the onboard water in the vehicle using the lab equipment at their disposal, and that could have made a difference.
As a sidenote, but relevant to this scenario, I lived in very remote areas of outback Australia for a while (cattle stations in SA and the NT), where the conditions would be similar to that of the desert in New Mexico. A few years beforehand, a couple got their 4WD bogged down about 70km off the main track (Oodnadaata track - itself just a dirt road). The guy stayed with the vehicle, the girl attempted to walk the 70km to the main track. He survived, she made it about 40km or so, before she perished. There's an interesting account of it here, and the obstacles to such an endeavour are clearly highlighted.
Mr. Liersch noted that the deceased had been carrying a rucksack and
also saw a two-litre bottle, which contained approximately 1.5 litres
of water. A later search of the rucksack revealed that she had been
carrying another five litres of water in a container, and another two
litre container containing 80mls of urine.
"The deceased was allegedly a student from Vienna who died after her
vehicle was bogged near Lake Eyre. She apparently left on foot and
perished approximately 40km from the vehicle. The extreme
environmental temperatures of between 43°C and 46°C suggest that her
survival time would have been limited under these conditions. The
specific gravity of urine alleged to have been retained with the body
was recorded at Coober Pedy at 1.030. The normal specific gravity is
approximately 1.020. The minimum loss of fluid under ideal conditions
is approximately 1200ml of fluid per day which must be replaced. The
total body water for an adult is approximately 40 litres and an adult
will normally become ill when the body fluid loss is approximately 4
litres or about 6% their body weight. Death will occur when body fluid
loss is about 15 litres. The urine is haemoconcentrated and appears to
have been saved in an effort to recycle water.
With that in mind, and considering their lack of survival skills, short of a minor miracle, Walter and Jesse were probably screwed.