NYT simply takes the number now earning less than the proposed new minimum wage of $10.10 (to be fully enacted by 2016) and declares that all employers will pay workers this wage, even if workers are not productive enough to generate marginal revenue product higher than $10.10 per hour. In addition, NYT ignores the likelihood that it will become beneficial for some firms to switch to machine automation rather than paying workers the higher wage.
Here's NYT, they call it "The Case for a Higher Minimum Wage," although they don't make such a case, they just assume an environment that couldn't possibly develop:
The political posturing over raising the minimum wage sometimes obscures the huge and growing number of low-wage workers it would affect. An estimated 27.8 million people would earn more money under the Democratic proposal to lift the hourly minimum from $7.25 today to $10.10 by 2016[...]NYT further fails to address the fact that there are now many unemployed because of the current minimum wage. Maybe NYT thinks an unemployment rate for youth of over 20% is normal.
This is not a new debate. The minimum wage is a battlefield in a larger political fight between Democrats and Republicans — dating back to the New Deal legislation that instituted the first minimum wage in 1938 — over government’s role in the economy, over raw versus regulated capitalism, over corporate power versus public needs.