The problem is that isn't what red states do, though.
Because of the welfare reform of the 1990's, federal welfare is no longer direct-to-recipient. Instead, it is now mostly given to states in the form of block grants because the argument was "states know better how to spend money than the feds" - a bullshit argument, of course. So the welfare reform law mandated that states need only spend 66% of the block grant on federal programs and can do what they want with the rest. So what do most red states do? Take the remainder of the welfare block grant to subsidize artificially low tax rates for (mostly) the wealthy. Because you see, tax cuts and low tax rates always lead to deficits, and since most of those red states have stupid BBA's, they have to raid the welfare block grant just to make up the revenue gaps that come from low tax rates. My state of GA is notorious for this, but we've seen it happen over and over the last 20 years. Most recently in Kansas, where they cut welfare to balance the budget that was thrown into disarray by the Conservative and Art Laffer-backed Brwnback Tax Cuts that failed to deliver on any of the promises made of them. Those tax cuts were so terrible that Republicans repealed them.
It's another example of Conservative fiscal terrorism.
TANF is a relatively small percentage of federal funds received by the states. For example, Georgia received $329 million in TANF funds and $12.6 billion in military spending. The blue states are not "subsidizing" Georgia because Georgia's tax system has no effect on defense spending.
Tax cuts and low tax rates do not lead to deficit spending unless spending increases faster than revenue which is what happened at the federal level.