Sherry,
I completely agree about the potential importance of this policy. My former colleague Raluca evaluated a child tax benefit in Canada:
Ionescu-Ittu, Raluca, M. Maria Glymour, and Jay S. Kaufman. "A difference-in-differences approach to estimate the effect of income-supplementation on food insecurity." Preventive medicine 70 (2015): 108-116.
As you'll see in the paper, a key aspect of the approach was defining the population who would benefit in order to identify the most comparable population who would not benefit to use as a convincing comparison. In her study, we used age of the child, because the Canadian policy has a sharp age threshold.
We also struggled w/ the question of what outcome might be affected in a short time frame (and also what was measured). Other outcomes that you might think would be responsive are mental health, developmental, or behavioral measures for kids, or mental health or perhaps certain health behaviors for parents.
Maria