No, they will not, and here is why.
1. They do hear from economists, and know that a MW raised that high that fast would kill the economy.
2. ANY MW that's supposed to be a "living wage" will end up simply chasing an ideal that can never be reached. First, jacking the MW increases inflation and within a short period of time erases any benefit. Secondly, those who got big raises and didn't lose their jobs and those who benefit politically from their votes will, in VERY short order, decide that whatever they set the MW to just isn't enough, and will insist on raising it yet again.
3. There is a significant number of people who would like to work and who would benefit from working, but don't need to be paid a lot to do so. Jacking the MW too high simply prices them out of the market, leaving them unemployed. You graduated from high school and want to start working? Great, just wait a few years until something opens up or enough experienced workers die to give you a spot.