That's the crux of the entire debate. There arguably is plenty of evidence of multipliers, but the problem is that when your lab is the entire society, there's no counterfactual - there's no control group. So you can never quite say that in the absence of the debt spending, the multiplier effect wouldn't have happened.
Anti-keynesians (hayekians?) point this out regularly and like to say that the burden of proof is on the keynesians, which will of course be impossible for the keynesians to ever prove. So that's where they get their handhold on arguing against keynesian theory. (Note I'm only a hobbyist with this stuff so my explanations may be way off - this is just my own sense of it.)
Now, there's something to be said for sometimes accepting something that is not potentially provably false. I think Darwinian evolution is an example of something that is not a strictly technical theory, but there's been such a body of experimentation over the years that you pretty much have to accept it as fact anyway.
And there's work done in modern Causality about how to tease out causality from correlation in the absence of counterfactuals. I've been trying to struggle through a causality textbook by Judea Pearl but it's really weird advanced stuff.
