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What you're saying is completely the opposite of the basic fundamentals of economics. 

GDP is a measure of economic activity.  It's made up of consumption (C), investment (I), government spending (G) and the trade balance of exports less imports (X - M). So

     GDP = C + I + G + (X-M)

Let's ignore the (X-M) part for the moment to keep things simple.

In year zero, we have our economy:

      GDP₀ = C₀ + I₀ + G₀

In year 1, our economy goes into recession.

GDP₁ = C₁ + I₁ + G₁

People aren't buying as much or investing as much as they were in year 0, so C₁ < C₀ and  I₁ < I₀.

That means, if government spending stays the same, obviously GDP₁ is going to be lower than GDP₀.  If government spending also falls, GDP will be even lower and the recession will be even deeper.  So cutting G is more damaging to the economy.

OTOH, if government spending is increased, it will offset at least some of the fall in consumption and investment.  GDP would be higher, and the recession will not have as much impact. Saying that stimulus spending has no impact on the economy goes against basic arithmetic.

The increase in government spending doesn't even have to be equal to the fall in consumption and investment to offset it.  There's a factor called the "multiplier effect".

When someone (whether a person, a company or the government) spends money on goods or services, it doesn't just disappear.  The person receiving the money will spend some of it on more goods and services. And then those people will spend more and so on.  The impact of the initial spending increase is multiplied.

So for example, when there's a recession and the government extends unemployment benefits to those effected, the unemployed can keep spending more than they would, so they spend money at Wal-Mart, which spends money on truck-drivers to keep its stores filled, and the truck drivers buy gas to keep their trucks moving, and the gas stations buy more oil and the oil companies spend more on marketing and so on...

This is the multiplier effect in action.  It is why stimulus is not just shuffling money from one sector to the other.  When the economy is running well, then yes - government spending can crowd out investment from the private sector.  But we're not talking about that situation - we are talking about when the private sector is not investing as much as it should be.

Fiscal policy has an undeniable impact on the economy - and it's why governments should run deficits in bad times and also run surpluses in good times while the economy is going well - so it has the capacity to run deficits in the bad times.

This not what the US government did over the last decade - it ran deficits while the economy was growing quickly, and this undermined its ability to cope when the recession hit.

But I suppose what you really want is a study about the current recession in the US, and whether the stimulus created jobs.  Well, there's this report by an economist at the Federal Reserve Bank of San Francisco, which says that the stimulus spending created or saved 3.4 million jobs over 2009 and 2010.

http://www.frbsf.org/publications/economics/papers/2010/wp10-17bk.pdf

This isn't an outlying estimate either. It is in line with estimates from the Congressional Budget Office and the Council of Economic Advisers.

If you're looking for reasons why the stimulus has not been as successful as creating jobs as was hoped, you might want to look at the size of the stimulus itself.  The US lost about $2 trillion in economic activity over 2009-2010.  The stimulus agreed on was about $800 billion, which was more than Congress had ever approved before, but it's obviously not enough to offset that lost $2 trillion - even with the multiplier effect.

You might also want to look at how the stimulus is distributed - does it go to the areas that will most improve productivity and help the economy?  Stimulus acts are passed by Congress, which tries funnels as much as it can into pork-barrel projects so it's popular enough to get passed.  But that's a problem with governance, not with stimulus itself.

There's a reason that when the financial crisis first hit, nearly every country in the world from China to Norway loosened fiscal policy. It's because stimulus done well works. The issue is how to do it well.