Answer: Wages would drop in certain industries.
Explanation:
The Fair Labor Standards Act of 1938 allows for a minimum wage provision and it is based on this that a minimum wage is set at the Federal level.
If this law is repealed, some employers would decrease the wages they pay their employees so that they can make more profits. This might work in certain industries especially ones that require little skill due to the number of people who want jobs in those industries.
It would not work in a lot of other industries and employees would simply stop working if they are offered such low wages based on the perception that their skills deserve more compensation.
Then there are the Unions who would try to protect their members from wage decreases and would therefore push back against the employers.
Bottom-line is that employers might try to reduce the wages but they would only be partly successful.