What is the dispute between Keynesian economics and Classical economics.
Quite a lot really.
Most people think Keynesianism means using fiscal stimulus when the economy slows down.
Don't believe me then read the General Theory yourself.
Keynesianism is using fiscal policy when there is a liquidity trap. What you ask is a liquidity trap?
It is circumstances when monetary policy doesn't work. In the 1930s it was deflation. now it is zero bound interest rates. I would also add when monetary policy is impotent such as in Australia's case during the GFC. the RBA eased rates BUT banks found it hard to get any funding, even with a Government guarantee, to lend money out.
The big trick is to ensure as the temporary stimulus runs out that fiscal policy doesn't become too strict and ruin any recovery such as the US in 1937 or Japan in the 90s.
In 'normal' times' monetary policy is the preferred policy instrument. Fiscal policy is only used to the extent automatic stabilisers kick in.( i.e. no large deficits).
Thus we see it is counter-cyclical.
Classical economics, on the other hand, emphasises always having a balanced budget no matter what the business cycle. As the budget begins to get into deficit because unemployment rises and tax receipts fall The Government cuts spending and/or raises taxes to attempt to maintain a balanced budget.
Thus it is pro-cyclical. In bad times it exacerbates a slowdown and creates a recession. you can even promote a depression like Ireland or Estonia.
In good times Keynesianism means much stricter fiscal policy that classical economics. See here for example. This means a larger budget surplus the stronger the economy.
Classical economics on the other hand means greater stimulation to the economy. This is because the government will either spend more money or cut taxes as more revenue comes in because of the stronger economy.
Now you ask what should be happening right now?
I think Jonathon Portes and Richard Koo both have a good take on that.
This means Australia has done an extremely good job since we got hit with the GFC. The stimulus was large enough to avert a recession and as the stimulus has finished the detraction from GDP has not been too large to offset the recovery.