Our busy lives prohibit us from thinking about much less understand various claims and proclamations about a variety of things. Consquently, if something is repeated enough we often mindlessly buy into it, even though we don't really understand. The so called "multiplier effect" is an idea that has gained currency in just this way. It is a myth. It is part of a discredited economic theory (Keynesian economics), but unlike the general theory that does get some things right now and then, this has the distinction of having no merit at all.
The economist John Manyard Keynes idea is that during a recession, heightened government spending will put more money in consumers hands (through public works, cash distributions etc.) and will stimulate the economy faster and greater than if left to its own devices. He said that if money were spent to move dirt from one hole to another, it would help activate the economy. Each dollar spent will result in a series of purchases as it passes through various hands, creating several additional dollars in economic activity. He named this the "multiplier effect." The conclusion is that the downstream effect of government spending is more jobs and more wealth. It is of course sheer and utter nonsense.
Think about where the government got the money to begin with. It either taxed someone or borrowed it. If something like the multiplier effect were real, would it not follow that taking this money out of the economy would reduce economic activity? The dollar coming from the private sector which was used in stimulating the economy didn't get spent by the private sector, and so that multiplier effect was lost. Does this effect exist only in government but not in the private sector? I won't even argue here that the greater efficiency found in the private sector's deployment of capital would suggest that if this effect could be quantified, it would be greater when executed in the private sector than by politicians. Let's just call it a draw, and with a draw the theory fails.
If the government could create a lasting increase in economic activity by taxing, borrowing and spending, we could just tax and spend our way to prosperity- a sort of never ending Ponzi scheme. Winston Churchill said that a country that tries to tax it's way to prosperity is like a man standing in a bucket and trying to pull himself off the ground by the handles.
The reason this idea gets promoted along with Keynesian economic theory is that it serves as cover for politicians to spend money. Democrats have lavished vast amounts of money on their constituents in the recent stimulus bill, all in the name of enriching you and me. I don't think so.