What money that the government can borrow is not invested in productive enterprise? There isn't a penny in a bank anywhere that is not invested each and every night.
Government borrowing just reduces the amount of funds available for productive investment and dumps them down a non-productive rathole. A government job creates no additional value -- it is an economic deadweight on the economy.
DING DING DING DING DING DING DING DING! Well, almost. In fact, much of money the government borrows isn't in productive enterprise, but would be if the government hadn't borrowed it.
Fundamentally, when a business borrows $100,000 and agrees to pay back $110,000 at the end of the year, it's doing so because it expects that use of that $100,000 during the year will enhance its productivity by more than $10,000. Business investing can only be successful if the money goes toward productive enterprise. Government borrowing gobbles up funds that would otherwise be spent on productive investments.
A great deal of assets held by banks are invested in fed funds, Treasury bills, tax exempt government bonds, agency securities and other government securities. Quite the opposite of an “investment” by your definition. During periods of slow or negative economic growth, the percentage of bank assets held in these sorts of assets increase as there is slack business and consumer loan demand and banks prefer low-risk investments during times of economic stress.
If one believes that economic recessions are caused by inadequate aggregate demand, having the government create “artificial” demand to fill the void left by consumers and businesses may make sense under certain circumstances. This is not a controversial opinion among economists, even free market conservative economists. Heck, even Hayek accepted this premise, although only for the short term.
On the other hand, Keynes assumed that these counter-cyclial fiscal policies would be used in the context of a government in structural fiscal balance. Moreover, he argued that the government should run a surplus during flush times. Clearly, these conditions do not exist today. If any economists suggests that the problem with the U.S. economy is one of insufficient demand or inadequate fiscal stimulus, I strongly suggest they seek immediate psychiatric care. Are you listening Herr Krugman?