Government costs are offset by taxpayer revenue. This 1.9 trillion is no different. Changing the minimum wage will impact taxpayer revenue.
One argument is that higher wages means a larger volume of taxes for that individual. If Americans were earning more, it would mitigate the increased costs by generating more taxes.
The problem is that they wouldn't be earning more despite being paid more. The amount of work a person is capable of doing is finite, while more money might motivate them to perform better under normal circumstances, this loyalty/motivation effect is lost when every job is required to pay at least that amount. At the end of the day, getting paid 100 times as much won't make people produce 100 times more.
Companies in response to the employees accomplishing a similar amount of work but costing twice as much per hour are forced to reduce hours and reduce staff. It would also accelerate the turn towards automation. Unemployed people wouldn't generate taxes. Some large businesses can afford to absorb the cost, some smaller businesses can't. All businesses that are just barely surviving will fail, like they would with any major increase in expense.
Maybe there's a sweet spot where paying more means more revenue overall, but I really doubt it's in the "double" range.