Today in class I did a poor job of explaining where Barro got his conclusion that the stimulus program was likely a bad idea from a costbenefit standpoint. Here is a clarification.
First, the assumptions on spending are that government spending has a 0.4 multiplier effect in the first year, and a 0.6 multiplier effect over two years. Part of the confusion in class stemmed from an improper interpretation of this assumption. The assumption can be broken down as: 1) the stimulating effect of government outlays lasts 2 years, 2) in the first year the multiplier effect if 0.4, 3) in the second year the multiplier effect is 0.2, for a total twoyear multiplier of 0.6. Instead, in class we assumed a multiplier of 0.4 the first year and 0.6 the second year  an incorrect read of Barro's article (in my defense, the article is not particularly clear on this point).
Second, the assumption on tax increases is that they have a multiplier effect on GDP of minus 1.1, which occurs with a one year lag.
Third, it is helpful to recall the basic national account identity:
GDP= Private Investment + Private consumption + net exports + government expenditures (government investment and consumption expenditures)
or:
Y = C + I + NX + G
Fourth, Barro assumes that the stimulus takes the form of $300 billion in incremental government expenditures in each of 2009 and 2010, financed on impact by borrowing from the domestic private sector, and ultimately financed by incremental tax levies of $300 billion in each of 2011 and 2012.
With these assumptions in hand we can fill out the table I drew in class today (figures are in billions of $):

2009 
2010 
2011 
2012 
2013 
Total 
Change in govt. outlays 
$300 
$300 
$0 
$0 
$0 
$600 
Change in govt. tax receipts 
$0 
$0 
$300 
$300 
$0 
$600 
Change in GDP 
$120 
$180 
$60 
$330 
$330 
$300 
Change in private expenditures 
$180 
$120 
$60 
$330 
$330 
$900 
Things to note: The 2009 stimulus effect on GDP of $300 billion in additional government expenditures is $120 billion (0.4*$300 billion). In 2010, you have the remaining stimulating effect of 2009 expenditures (0.2*$300 billion or $60 billion) plus the immediate stimulating effect of 2010 expenditures (0.4*$300 or $120 billion), for a total of $180 billion. In 2011, you have the remaining stimulating effect of 2010 expenditures, or 0.2*$300 billion=$60 billion. That's where that mysterious $60 billion came from.
Another thing to note is that tax increases do not enter the calculus other than through their negative effect on private expenditures. The taxes go to reimbursing the borrowing that went on in 20092010, so they are a net transfer from taxpayers to the creditors of the US government (i.e. taxpayers).
Where does that leave us? If you sum the columns horizontally, you get $900 billion in private expenditures that is destroyed by the stimulus, and $600 billion that is created, for a total net loss to society of $300 billion. This is what Barro correctly concluded. What I mean by correctly is  the calculation is correct if the multipliers that he assumed are right. While some will feel that the spending multiplier is perhaps a bit low, others will observe that Romer and Romer came up with estimates of the tax multiplier that are greater (in absolute value) than Barro's. So when all is said and done, the ballpark calculation is probably not too far from being right. If you disagree, feel free to come up with your own costbenefit calculation, based on your own assumed multipliers.
Voilà!