Ask the employer to correct the mistake, and if they fail to do so, find a different employer. A good employer will not stand in your way to getting a license. Take whatever time they'll give you and move on.
Depends on what state your in. Different states have different rules. If you still work for this employer he should just redo the paper work and you'll be good to to go. If you don't work for this contractor and he won't change the reported hours I'd call the state licensing office and see what your recourse is.