There is a growing body of research that shows why cash matters for families. The file attached at the right TANF-Talking-Points-For-States.With-Cites.docx (live.com) provides talking points that you can use to make the case for why increasing cash benefits will positively impact children and parents and reduce costs for human service agencies, especially through lower costs in child welfare.
You can find data on state benefit levels in CBPP’s annual paper on benefit levels: Increases in TANF Cash Benefit Levels Are Critical to Help Families Meet Rising Costs | Center on Budget and Policy Priorities (cbpp.org). The tables in the appendix provide a comparison across time and across states. You can also ask an income security staff person if you need more updated data or would like the data in a spreadsheet to make it easier to create visual charts. Comparisons with benefits in neighboring states or states with similar characteristics can be a powerful way to garner support for an increase in benefits.
This CBPP paper also provides a good summary of why cash matters: Economic Security Programs Help Low-Income Children Succeed Over Long Term, Many Studies Find | Center on Budget and Policy Priorities (cbpp.org). (There is more recent data available on this topic. You can check with CBPP staff to see if an updated synthesis of the research on this topic is available.)
This report from the National Academies of Science, Engineering and Medicine is often cited as evidence for why cash matters. The report is quite long, but concludes that “poverty causes negative outcomes for children, especially if it occurs in early childhood or persists through a large part of childhood.” The National Academies Press | A Roadmap to Reduce Child Poverty – Data Explorer