It turns out that parents do far worse under the TCJA than the population as a whole, and making the expiring credits in the TCJA permanent only modestly changes this story. More than 40% of families with children face a hike under TCJA in 2027, even with the security of permanent filer credits and assumptions about the benefit of corporate tax cuts.
As always, I'm using the excellent Open Source Policy Center (OSPC) TaxBrain model for this analysis.
To set the table: under the TCJA as written (what I'm calling "TCJA law"), 72 million filers or about 37% of the total get a direct tax increase in 2027. This number falls to 50 million, or 26%, if I distribute the benefit of TCJA's corporate tax cut similar to how JCT did in their score of TCJA last week. 
But filers with children under 18 fare much worse than the overall population. In 2027 I estimate that there are 24 million families with kids who see a direct tax hike, 55% of all such families. Distributing the corporate tax cut lowers this by 4 million to 20 million, or 45% -- still a far higher proportion than all filers writ large.
In fact, both with and without the corporate income tax, the median tax change among all families with kids in 2027 is roughly $0 under TCJA law, though there are wide disparities in outcomes even within the same income band.
The rebuttal made by supporters of TCJA is that there are benefits phased out in the legislation to save money that, in reality, would not expire, specifically the filer and nondependent credit. Under TCJA these expire in 2023, and doing this rather than keeping them permanent saves around $200 billion over 10 years. But the claim here is that Congress will feel compelled to extend them before they expire, as it does with many other ostensibly "temporary" provisions in the tax code.
I wanted to test the substance of this argument, so I also simulated what would happen if Congress made these two credits permanent. Would families with children be that much better off under the TCJA?
The results below show that the answer is a modest "yes". About 1.9 million more families would get a tax cut in 2027 if Congress made these two credits permanent ("TCJA Policy"), an additional 4% of all families with kids.
We can see by taking the difference between the TCJA Law and TCJA Policy dispersions to find out who the net beneficiaries are of making these credits permanent. Unsurprisingly, families making under $100,000 in 2018$ see almost all the benefit.
What this tells us however is that a lot of parents will be worse off under TCJA even if the filer and nondependent credits are made permanent. That's because the law makes several changes -- elimination of the personal exemptions, a rise in the lowest bracket to 12%, a slower inflation adjustment for benefits like the Earned Income Tax Credit (EITC) -- that hurt families.Often the changes the law makes in support of families such as the increases in the standard deduction and the child tax credit, and the introduction of the filer and nondependent credits, are not enough to make families whole.
In other words, even if these credits become permanent and even giving the plan the benefit of its corporate tax cuts, more than 40% of parents face a tax hike under the TCJA.
The good news is that members of both parties have introduced plans that could serve as templates for shifting the TCJA towards helping parents, including the Bennet-Brown plan from Democrats and Rubio-Lee among Republicans. The details of these plans differ but the broad strategies involved -- an expansion of the child tax credit and/or EITC with some mechanism for making the child tax credit more refundable -- are compatible.
What's clear though is that the TCJA as written poorly serves parents. As the House and Senate negotiate, they should overhaul it to make it a true pro-family and pro-child piece of legislation.
 For the purposes of this post, I'll graph the results of the corporate-tax-inclusive analysis, but it's important to remember that the benefits of a corporate tax cut to families are 1) indirect (i.e. in the form of higher wages or investment returns rather than lower taxes owed on a 1040), 2) the subject of fierce disagreement in economics, and 3) likely greater than zero but sensitive to how the tax cut is financed.