I live in Florida, so they only non-federal tax I pay is property tax. (Excluding sales taxes, of course.) Every year, I get a full breakdown of exactly what mils go where with the bill. I bet we would have something similar at the federal level by now, except that stupidly we have to do the whole "guess the number I'm think of" game with the IRS instead of them sending a bill.
I personally think the engagement part would come instead from "My $5000 in tax went through the system and was eventually spent on a federal initiative I don't agree with" (or since it's all granular: "only $13 of that $5000 went to anything that benefits my community?"). No, I'm not saying that everyone will care, but I think that more people will care.