I'm not sure exactly how taxes work at the level of the states... but I kind of doubt this strategy will have any significant impact on the federal budget, considering that most people have already paid their taxes for the year. They haven't filed their taxes - but anyone with a W2 automatically has part of each of their paychecks sent to the government preemptively. That's why most people get a tax return - the government takes what it expects you owe, and then when you file your taxes, most of the time the actual amount you owe is less than that, so the government gives you your money back.
Maybe there are ways around this. Maybe you can opt out of your employer paying your taxes for you? Maybe your employer can decide not to pay? Maybe the money you've been paying for the year has actually been held by the state, and they can choose to withhold it? I don't know. But for most people, this idea is a non-starter, and they will file their return as usual and get their refund.