This is the opposite of the truth. Supply and demand don't suddenly stop clearing because the government cuts spending[1]. Stuff the government consumes is stuff that nobody else gets to consume no matter what the tax rate is. Taxes and debt are just how you pay for it without inflation. This isn't a radical claim, it's Econ 101 stuff, and there are countries that have had economic expansions while running high taxes and surpluses.
[1] Actually government spending does affect the balance of non-government supply and demand, an observation that is a fundamental part of the Keynesian school. But that's a second-order effect, not a first order one.
Maybe I should have been clearer. If the government is spending more money then they are pulling in in taxes, then how does a cut to government spending translate into money in the pockets of the citizens?
If Spain was pulling in $2-billion in taxes, and spending $4-billion by borrowing the deficit, then how does a reduction in spending down to $2-billion give money back to the people? It stops the bleeding of money into debt, but it doesn't give money back to people to then spend on goods/services.
[1] Actually government spending does affect the balance of non-government supply and demand, an observation that is a fundamental part of the Keynesian school. But that's a second-order effect, not a first order one.