I disagree, we are talking about minimum wage earners, not skilled workers. Minimum wage earners are predominantly in unskilled jobs that require little or no training, so there would be little loss in productivity.
Increasing the working hours of those that are underemployed is also a good thing, if they are the experienced workers. Those experienced workers would also be paid more, for doing more work, which then flows back into the community. Either way it is a win/win situation, both for the local economy, and the lowest paid workers.
I don't live in the US so don't know what your conditions are like, on the ground, so to speak. What I do know is that giving a rise to the lowest paid workers will not send a small businesses, or a country broke, but,giving tax cuts to the wealthiest, and handouts to big corporations, will.