As others have pointed out, this can't (even in theory) work. And historically (on years when it's been tried) it didn't in fact do any good.
The reason this can't work, is that it does NOTHING to lower overall usage (which might effect "supply and demand"), and merely shifts the purchasing to a different day. And worse yet, because people didn't spread out usage out as evenly (because people were trying to skip buying of gas on this day), it actually has the potential to cause a slight spike in demand on days around the 15th (thereby actually causing prices to go up a little)!
IMHO this is a cute "feel good gimmick" only. The only positive things that this could possibly do (even if all goes well), is possibly get a few more people thinking about gas prices and/or send a "symbolic message" that people are "serious" about this issue. But more likely than not, the only message this will really send, is that people are stupid sheep that can't really do anything that matters. And the whole premise of this exercise (in futility), is so flawed, that (far from getting people to think) it has the significant danger of distracting from other things that might actually do some good (for example, techniques to get better gas mileage, and therefore have to use less overall gas)...
What are people thinking?