If the minimum wage is set at or below what would normally be negotiated for an unskilled, untrained workers, it has no impact other than for n individual is not very good at negotiating, in which case the minimum wage helps him/her. If on the other hand, the minimum wage is set at higher than what would be worked out by the law of supply and demand, it helps those individuals who get the jobs, but results in employers cutting back employment (using automation, outsourcing, etc.). For example if the minimum wage is $10/hour, an employer will choose not to hire an employee who is not producing $10 of extra profits every hour – the higher the wage, the harder it is to justify the employee.
The Democrats believe that most employers are making a huge profit on each employee, and therefore the employers will not reduce employment if forced to raise wages. The Republicans tend to feel that the law of supply and demand works so that wages stay in sync with profits, and therefore raising the minimum wage about what would be produced by a free market results in lower employment.