A quick Google search found a handful of links to empirical research supporting that idea.
Specifically: The authors examine 23 years of household spending data and find that for every dollar increase for a minimum wage worker results in $2,800 in new consumer spending by his or her household over the following year
That article is not talking about the multiplier effect. It is talking about consumers consumption smoothing...buying automobiles after the minimum wage goes up because there has been a permanent increase in their income. From the article:
"Our estimates are silent about the aggregate effects of a minimum wage hike."
I've read a lot of the econ literature in this area, and have never seen a defense of the minimum wage on the basis of multiplier effects. Too few people are working at the minimum wage. And, the minimum wage is too blunt of a instrument to try to counteract business cycles.
That's a local effect though (your quote). The money that goes in that workers pocket has to come from somewhere else. Also raising the minimum wage possibly causes some (slight) additional unemployment.
So what's the overall stimulus effect on the economy? Unclear. It appears as if the second study on the page you linked to might try to address it, though it looks to me like more of an advocacy paper than an impartial study. That's just from a quick glance though. I will try to read further.
My overall impression of the minimum wage debate is that it has a very high ratio emotion :: impact. Whatever overall effects it has on the economy appear to be quite small (almost within the noise), and yet it always generates a lot of intense argument. There's lots of signaling going on here I think.
