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Data4Democracy
Poverty/Welfare metric
Might I suggest the current population survey which is described here?
Note that this is sampled data, but it's got excellent history. Another thing to point out: census data is rich but stored in what has to be the most arcane format possible. Giving it a little TLC opens the data for a much bigger audience.
It is worth noting that it's big-ish: 144mb per month going back to 1994 (!). Your best bet here may be either (1) provide download and ETL scripts or (2) host the data in cleaned up format.
If you think this is in line with your plans, I'm happy to put something together.
I have state level unemployment and snap payment error rates available on kaggle. I could compile more data from the bureau of labor if it helps with this. I'm pretty interested in this vs perception, since I grew up in rural TN where many people are convinced that many people cheat welfare, and is a common thread when discussing politics.
These are yearly, regional reports on homelessness from point-in-time counts and other measures. https://www.hudexchange.info/programs/coc/coc-homeless-populations-and-subpopulations-reports/ Not a timely source, but maybe useful for historical purposes.
The Gini coefficient (Wikipedia) could be useful for looking at income disparity between different socioeconomic groups. This is all I could find as far as government data tracking the index but it would be easy enough to implement a script on our end and generalize it to different socioeconomic groups we're interested in.
CPS is not as frequent as I would like, but it's a good start. Maybe we can calibrate something higher frequency and now-cast it.
I'm fine with the size of the data, we have lots of offers for free hosting/storage.