When Mr Price announced the move to staff, it was greeted by enthusiastic applause.
But the honeymoon did not last long. Some clients objected to the "socialist" gesture and withdrew their business from his company, Gravity Payments.
Two valued members of staff resigned in protest at the decision not to increase their pay and maintain some sort of differential among employees.
Mr Price said: "I'm working as hard as I ever worked to make it work. There's no perfect way to do this and no way to handle complex workplace issues that doesn't have any downsides or trade-offs."
Pay and jobs are important issues in the presidential election campaign. Hillary Clinton is supporting a $12-an-hour minimum wage, while Bernie Sanders, the Vermont socialist senator and her strongest rival, is calling for the current $7.25 to be raised to $15.
On the Republican side Donald Trump is in favour of the current minimum wage and opposes any increase, while Scott Walker, the Wisconsin governor, described the minimum wage policy as "lame".
Ted Cruz also opposes the minimum wage, while Jeb Bush says it should be left to individual states to decide.