Sometimes economists who support austerity have clear ideological or political motives. However I often come across economists who do not have these motives, and yet are deeply suspicious of the idea of Keynesian stimulus. In other words, they are economists who are quite happy to acknowledge market failure, and embrace the idea that governments have an important role in helping to correct that failure, and yet they are unhappy with what Jeffrey Sachs calls ‘crude Keynesianism’. (For a detailed critique of this Jeffrey Sachs piece, see this post from Mark Thoma.)
Where does this suspicion come from? Often there seems to be a view that the austerity/stimulus debate is a distraction from focusing on more important, longer term problems. Oddly this view is asymmetric: I do not think anti-austerity economists deny that there are also important longer term problems. I also think longer term issues are more difficult to fix at times of austerity, so in that sense the short and long term solutions are complements, not substitutes. There is the notion that some have that we need a crisis to get things done, but perpetuating and mis-diagnosing the crisis is precisely what those who want to use debt scare stories to reduce the size of the state are trying to do.
A particular and important example is a concern about high or rising government debt. Government debt is almost always a long term problem, whereas deficient demand should just be a short term problem. As regular readers of this blog will know, my current views about the (un)desirability of government debt in the long run are quite radical, but I have no problem combining this with a belief that in certain circumstances fiscal policy should be used to stimulate (or in the Eurozone, also cool down) the economy. 
There is an understandable concern about debt and markets. That concern should not be dismissed lightly. I remember being asked by economists working for the UK government in 2009 just how far can we let debt rise before markets panic? I knew that my answer, which was that in a balance sheet recession there was a higher demand for government debt (particular when it was accompanied by a flight to safety), was based on a solid macro model. But though I thought the chances of my being wrong were small, I also knew the costs of my being wrong could be very high, which should make anyone cautious. Now I am much more confident, because events have vindicated the model.  However I recognise that some people are hyper risk averse, or believe markets are totally fickle, which is partly why I have always stressed that fiscal expansion can be done without issuing more debt. So if this is your real concern, become an advocate for balanced budget fiscal expansion or other, more innovative, changes in the fiscal mix.
I suspect an equally important reason why economists are sometimes unenthusiastic about fiscal stimulus is that they have been trained to misread the problem we are currently dealing with. This is not just the idea that monetary policy rather than fiscal policy is the stabilisation tool of choice. More fundamentally, it is the line promoted – consciously or unconsciously – in almost every textbook that economic downturns are ultimately self correcting. We have a business cycle because prices are sticky, but eventually prices are flexible, so we are bound to get back to full employment once prices adjust (which cannot be that long).
The best thing to say about this message is that it is incomplete. It should say that what gets us back to full employment is monetary policy. Having an appropriate monetary policy is a necessary condition for returning to full employment. A monetary policy that, for example, kept real interest rates constant would not get us back to full employment following a permanent negative shift in aggregate demand. The moment you understand this, the seriousness of the zero lower bound coupled with inflation targets (which put a lid on inflation expectations) becomes apparent. We are not dealing with a normal recession that will end pretty soon, we are dealing with something that could last much longer.
So for someone like me, what I see at the moment is very simple. We have demand deficiency, and the normal means of correcting it is broken. We luckily have a backup system, but the levers of that system are being pushed in the wrong direction. What is worse, this backup system is not some mysterious or controversial mechanism – it is what we teach to students day in and day out. So to push the levers in the wrong direction just makes a mockery of macroeconomics.
 There is a concern about transition and persistence. That fiscal expansion today will be politically difficult to undo, and so will increase the longer term political challenge. I think that is one good reason for focusing on government spending rather than tax cuts or transfers, and more specifically on government investment, in any stimulus package. There are of course other good reasons for doing this.
 And because we have Quantitative Easing.