The issue is that this is a regressive tax. In other words:
The less money a person makes, the higher percentage of their income they have to pay. Sales taxes are usually called regressive as poor people spend a higher percentage of their money, than rich people.
The tax rebate sounds like a good idea. Even if your deductions exceed what you owe in taxes, you can see up to $1,200 a year in tax credits. But then that doesn't sound as good when childcare can cost between $3,582 to $18,773 a year, for an average of $11,666. Not only that, the money is given after tax season, not monthly, like when your bills are due.
Many working class families wouldn't be able to take advantage of the tax deductions because their taxes are too low. That's not to say it won't benefit the working class, but in this case, the more money you make, the more benefit you'll get.