The plan has a very interesting table regarding multipliers. A multiplier is an estimate of the "cumulative impact of various policy options on GDP over several quarters"
Notice that spending can have a minimum multiplier of 1 -- meaning each dollar spent adds that dollar to the national GDP total -- and a maximum multiplier of 2.5 -- meaning each dollar spent adds 2.5 dollars to total GDP. The truth is most likely in the middle somewhere.
The reason for this multiplier effect is simple. Government body buys $1 of goods. Someone has to sell those goods to the government. In addition, someone has to make those goods which are then sold to the government. And someone has to extract the raw materials to put into those goods. In short, a purchase stimulates the entire chain of production from extraction to sale. Hence the possibility of a higher multiplier.
First, these estimates are from the Joint Committee on Taxation, whose website is here. Notice that with tax cuts the multiplier is higher for lower and middle income tax cuts than upper income tax cuts. Why? A tax cut for lower and middle income people effects a larger amount of people -- that is, there are more taxpayers in the middle income brackets than higher tax brackets. According to this table from the Tax Policy Center there were 1448 tax units in the 28% tax bracket in in 2007 compared with 73 in the 33% bracket. Basically, this is simple math.