A 150 should work fine as long as they are the only primarily pod picking fish (all fish will pick some).
If you add plenty of wrasses, pipefish, seahorses and the like food may get sparse.
How low in tank size you can go depends largely on your skills and dedication.
There are people here who manage to keep mandarin pairs in 10 gallon tanks.
I personally find that too small, not because of food (pod) reserves but rather because the mandarins need some room and especially height for their mating dance.
I have a pair in a 25 gallon cube now for a year. It was only planned to be short term but getting the new tank took longer than I had planned for. Nevertheless they handled it OK, though they are not spawning in there. In about a month they will finally go into a 100 gallon tank.
I see the limit space requirement for a pair at 40 to 50 gallon with a minimum water height of 18 in. This is just for them to feel comfortable in regards of space.
Food reserves are an entirely different issue. You should ideally have a refugium (with no fish in it!) from where pods can populate the tank.
You may also have to supplement their food with live or frozen brine shrimp and frozen Mysis. All I had sooner or later picked up eating frozen foods.
BTW: buying pods will get expensive in the long run. It is better to set up a few cultures somewhere and produce what you need in house.
