"WHY is Big Government a bad thing"
Explain 'big government.' A state with extensive social welfare, for example, is often touted as 'big government.' There is no Constitutional provision for an extensive social welfare state. The United States government is subservient to the United States Constitution; it is the contract by which the United States government was created and the one by which it must abide. By and large what is referenced as 'big government' is not in accordance with the Constitution.
"and, in an age of globalization and with the enormous breadth of the US's power and needs"
The United States Constitution must be upheld no matter what era, epoch or age in which we find ourselves residing. The age of globalization neither renders obsolete nor finds incompatible Constitutional ideals or statutes. The two superficially-conflicting ideas of a 'small government'-style Constitution and a global era are not contradictory.
"how would you manage the largest military in the world, one of the largest economy's in the world, nuclear arsenals, and the role of being one of the two great superpowers of the world with a SMALL government?"
For one, downsize the military. Cut military spending substantially. The United States can still be the pre-eminent military power it wants to be in absence of a substantial portion of its "defense" budget. We can defend this country with a substantially smaller military, and we can even defend the sea lanes and air space for international shipping without the majority of our budget. Most of our budget goes to finance unnecessary and extremely costly wars -- wars which, on top of the obvious drawbacks of making enemies worldwide, losing valuable American lives and spending valuable American tax revenue, are not even Constitutional themselves.
Nuclear arsenals as well. The line by the neoconservative war hawks that says "If we downsize our arsenal first, everyone else will just break their end of the deal!" is ludicrous. We can destroy the world several times over -- if not literally cause catastrophic damage to every corner of the world, at least wipe out so many people with nuclear weapons that the world as we know it would cease to exist. What's the point? Even in an absolutely insane scenario where we REALLY decided we wanted to destroy the world, you only need to be able to do that once. And honestly... when are we ever going to use nuclear weapons? We need some to keep anyone else from getting stupid ideas, sure, but we don't need... what is it, 5000? That's absurd.
The economy does not need the kind of heavy central management that 'big government' implies. Keynesian economic models -- the kind which this country has by and large followed since the early 20th century -- were not, by Keynes's own admission, blueprints for long-term economic management. And yet that is exactly what we have done. Furthermore, government interference in the economy is Constitutionally limited.
Perhaps the most important aspect of the economy that small government would fix is the Federal Reserve System. This largely-unaudited behemoth is responsible for the boom and bust cycle that often gets blamed on "free-market capitalism" by artificially adjusting interest rates. It is also the party responsible for inflation, which can only occur with an increase in the money supply. A true small government would be one without the Fed, and would be one with a much better managed economy.
Of course, it doesn't stop there economically. Corporate welfare has to go as well. Corporations do not deserve any special favors from government. That is not free-market capitalism as a small government would have it; that is egregiously pro-big business, and not small government. That is big government of the right, not of the left... but big government all the same.
The tax code needs a lot of reform as well. Though it would technically be a "tax increase," I very much support the Democrats' efforts to close tax loopholes. I would probably argue for tax cuts once the loopholes are closed and the tax code is simplified, because I suspect that when it's all said and done we can lower taxes on everyone. But it is definitely wrong to raise taxes on everyone and then leave loopholes only one sector of society can exploit.
"And keep in mind all those lovely deficits and debts that our large amount of military spending has produced...how are you going to fix THAT as well?"
You fix your debt problem by creating and maintaining budget surpluses on non-debt spending. That is, make sure you're taking in more money than you spend on other programs, and put the rest toward paying your debts. I find it interesting that the challenge is posed as though small government is the form of government between small and big that would supposedly have trouble with spending. Small government inherently spends less than big government.
You fix the wars by getting out ASAP, and downsizing the military substantially. That takes a lot of pressure off of government trying to make ends meet. You then cut spending, reform the tax code and see where that gets you. New taxes should not be taken off the table as an option, but should be an instrument of last resort once your spending has been cut. Tax cuts and hikes should both not be handed out unequivocally but should be decided upon at the end of the process. You adjust your revenue flow after you reduce your budget down to essentials, and if you happen to have surplus, you decide whether or not to cut taxes or increase spending. If you happen to have deficits, you raise taxes before putting us any further in debt.
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I believe that the above blueprint is a blueprint that is in line with true small government philosophy as a conservative would have it, and yet one that is also sensible and recognizes the reality of the situation we are in right now.