If the purpose of the minimum wage is not to ensure that employees who work on it are making at least a decent living, then the minimum wage has no real purpose. By your logic, eliminate the minimum wage and let companies decide what to pay people, living costs be damned.
The "repercussions" I assume you're referring to might be the conservative talking point that raising the minimum wage will cause massive layoffs, which has been suggested in studies to be patently untrue. Wage increases tend to lead to lower employee turnover, saving companies in hiring and training costs, and at worst lead to modest price increases for consumer goods. It is not an incentive to "climb the social ladder" to force workers to live on stagnant wages while the national cost of living continues to go up. That "use your shitty job as motivation" rhetoric is a bullshit tactic (do you think people just WANT to work in fast food forever, or is it possible that they do those jobs to support themselves as they go through college or trade school or simply pursue better opportunities?) and punishing the lower classes with 40-hour work weeks but little financial gains doesn't spur people magically into some endless field of higher paying jobs.
Living costs continue to rise, gas prices continue a gradual trend up, college tuition continues to go up. A lot of people in minimum wage jobs are attempting to put themselves through higher education. The CBO estimates that raising the minimum wage to $10.10/hour would give 17 million Americans a raise and increase net real income by $2 billion. Put more money into the hands of consumers, consumers inject that money into the economy, demands increase, supply increases, companies expand and job levels increase.
People need to get the fuck over the idea of unskilled labor being paid a decent wage in the modern economy. Countless economic studies have suggested that the benefits outweigh the costs. It's not the worst thing in the world for multi-billion dollar corporations to pay the human beings that make their business possible a modest amount of money to afford a basic lifestyle. Jesus fucking Christ, people.