An alternative would be to get the federal government out of it altogether.
They can simply come up with a budget, divide the number by the population, then charge the states based on population.
At that point you have a single number: The federal budget is $10,000 per person in the US, for example.
The states can collect it any way they like, and turn it over to the feds.
This solves a couple of problems:
1) no need for federal intrusion into personal lives anymore. The government interacts with the states only.
2) The states have control over the money. They give it to the federal government, not the otehr way around. The fed can’t withold money from teh states for political reasons.
I dare say that would change the states’ interest in census head counts and illegal immigration.
In case you've forgotten, that approach to government funding is one of the big reasons why we live under the Constitution now, rather than the Articles of Confederation....