As I understand it, in a sensible world we would run surpluses in good times and then spend that money in down times. In doing so we transfer jobs through time, thus smoothing out the ups and downs. This can be particularly useful in disaster situations. Unfortunately, we run nothing but deficits all the time regardless of who is in power. In any event, this is a pointless paragraph because this is not the world we live in and it addresses general Keynesian principles and not the multiplier directly.
So as I understand the actual argument about multipliers, it is your basic loop. How much of the extra spending is spent again, and how many times that loop repeats itself will vary based on general conditions and who gets the money. Under the right conditions and with the right kind of spending, you can get money into the hands of people who spend it like crazy and the loop goes on for quite a bit. In this scenario, the "multiplier" will be greater than 1. In other words, I do believe the multiplier is real.
So what about stimulus spending to take advantage of the multiplier in times of crisis when we weren't running surpluses first and basically borrow or print the money? I think it is pretty clear to everyone printing money doesn't create wealth, but it creates money. In theory, if the multiplier on that money is large and the economy is hurting badly, this could be worth it. Borrowing money can be viewed only as creating future taxes (although that view is highly theoretical in my opinion, based on what I see us and other nations actually do). But the key is, when faced with certain conditions and certain kinds of spending during those conditions--can you hit a multiplier that helps you come out of the hole more quickly and thus be worth it in the end...despite the problems with having not run surpluses first.
I think the answer is yes, you can. But it is far from some magic thing that will fix everything. And it isn't easy to do.
That said, I'm not an economist I just read the paper and blogs. I'm an idiot.