Ramesh below is absolutely right about the case for the Lee-Rubio amendment making the child tax credit refundable against both income and payroll taxes, and about the weakness of the case against it.
If there’s a point I’d press a little further it would be the distinct appropriateness of allowing the credit to reduce the payroll-tax burdens that lower-income working parents now shoulder. The case for the child credit is very much connected to the nature of our entitlement system, and the uneven way in which it distributes the costs of the intergenerational bargain at its heart. There’s no avoiding that unevenness entirely, but it can be mitigated, and Rubio and Lee are proposing one way to do that.
In essence, the middle generation in any society always supports the youngest and the oldest in that society, who cannot support themselves. But while we now socialize a significant portion of the older end of that bargain (so that today’s workers help fund the retirements not only of their own parents but also of all elderly Americans through their taxes) we quite appropriately don’t socialize the younger end in the same way (so that parents bear the costs of supporting their own children). But that means that those members of the middle generation who are parents also shoulder a greater share of the intergenerational bargain between the middle generation and the elderly—they pay to help all of today’s retirees and also to raise the workers who will pay to help all of tomorrow’s retirees. Lee and Rubio are suggesting that they should therefore be permitted to keep a modestly greater portion of the money they earn, and that it may be especially appropriate that they get some relief from the payroll tax, which is both the heaviest federal tax burden lower-income workers face and a tax that (on paper anyway) exists specifically to help fund Social Security for the elderly.
This would be tax relief in one of the places where it’s most needed and appropriate.