If we look at federal spending as a proportion of each state's overall GDP, we find that the recipients are not exactly evenly distributed:
Source: Pew Charitable Trusts (based on data from 2004–2013)
This is all federal spending, so these totals are a combination of military spending, social welfare programs such as Medicare, and ordinary civilian federal spending, including civilian research facilities and other programs funded by federal grants.
These are proportional numbers, so they are a function of both the amount of federal spending as well as the overall size of GDP. So, in California, for example, which receives immense amounts of government spending, is nevertheless a state where federal spending is offset by a very large private sector. In a more rural state with few major private industries, such as New Mexico, the state shows up as being highly reliant on federal spending.
By this measure, the state most reliant on federal spending is Mississippi where federal spending is equal to 32 percent of the state's GDP. The state least reliant on federal spending is Wyoming where federal spending is equal to 11 percent of the state's GDP:
Source: Pew Charitable Trusts (based on data from 2004–2013)
The above measure gives us a sense of how much federal spending is taking place relative to overall economic activity. But, it tells us little about how much the feds are spending in each state relative to the tax revenue being produced in each state.
To discover that, we need to compare federal spending to tax collections from each state. So, I took gross tax collection by state, and then subtracted refund totals. I then compared the "net" collections to Pew's total federal spending data in each state. (The tax data used was 2013 data.) We can then measure the result in terms of dollars spend in each state per dollar in tax revenue collected. States that have a value of less than a dollar in the map below receive less than a dollar in federal spending for every dollar in taxes paid from that state. So, for example, Ohio receives 91 cents in federal spending for every dollar collected in taxes from Ohio:
I've divided this graph up into "net tax payer states," "break-even states" and "net tax receiver" states. The lightest shade of blue are states that, by far, pay in more than they receive back, such as New Jersey and Minnesota. The next lightest shade of blue are states that are more or less "break even" in the sense that spending and tax collections hover somewhat around a 1-for-1 relationship. The darker blue states are states that receive considerably more in federal spending than they pay in taxes.
Here are all states, including values:
Naturally, these values aren't spread evenly within the states themselves, either. Areas that are more rural and reliant on agriculture will tend to be net tax receiver areas both because farmers and ranchers receive a lot of government subsidies, and also because agricultural work tends to have lower productivity than urban work.
Urban areas, in contrast, produce most of the tax revenue, so highly urbanized states will tend to more often be "break even" or "net tax payer" states.
Other Considerations
One thing that must not be ignored is the fact that the US government spends more than it takes in nationwide. During 2013, for example, the federal government spent a dollar for every 80 cents it took in via taxes.Nationwide, the tax-spending ratio is not one dollar, but it about $1.20. So, states that are getting around $1.20 back for every dollar extracted in taxes are really just at the national average.
This is being made possible by old-fashioned deficit spending and also by monetization of the debt which the Federal Reserve facilitates by expanding the money supply. Once interest rates rise or the international value of the dollar begins to fall significantly, this sort of overspending will no longer be possible, and many states will find themselves in dire straits. (States that are "net tax payer" or "break even" states will adjust the best to any significant disruptions in federal spending.)