The free market is already effectively making the minimum wage at something around $15/hour. Many major companies that require little/no experience have starting wages at or about $15/hour. If you are an employer and try to pay your employees something less than $15/hour, you will have difficulty finding and retaining employees.

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Raising the statutory minimum wage is not possible via budget reconciliation. Senate rules are clear on this. If Democrats want to raise the minimum wage, they will need to negotiate with Republicans. With that being said, Republicans agreeing to raise the minimum wage after receiving some concessions is not entirely unrealistic due to my statement above.