If Obama is not re-elected in 2012, it's overwhelmingly likely that a Republican will take up residence in the White House come 2013. For progressives, this would be a disaster.
This makes "How does the deal affect Obama's chances of re-election?" a fair question.
As it happens, economists and political scientists have given us mathematical models that yield an answer this question. I work through the math after the jump.
The Fair Model predicts the incumbent party's share of the two-party vote based on a range of political and economic variables. The formula that pulls these together is complex, but many of the variable values are now known, such that we can predict the 2012 Presidential election outcome in terms of just a few economic variables as:
Vp = 48.39 + 0.672*G - 0.654*P + 0.990*Z
where
Vp is Obama's percent share of the two-party 2012 Presidential election vote,
G is GDP growth per capita in 2012,
P is the 2012 GDP deflator, which measures inflation, and
Z is the number of quarters between now and the election where GDP growth is greater than 3.6%
This equation appears on page 12 of Prof. Fair's Nov 11, 2010 update.
Using Fair's forecast of 1.42% for P (inflation) lets us predict Obama's 2012 vote share entirely on the basis of economic growth forecasts:
Vp = 47.46 + 0.672*G + 0.990*Z
So, based on current economic growth forecasts, how will Obama fare in 2012?
The Federal Reserve Bank of Philadelphia's Fourth Quarter 2010 Survey of Professional Forecasters gives the following forecasts of quarterly GDP growth through 2012:
2010
Q4 2.2%
2011
Q1 2.4%
Q2 2.7%
Q3 3.3%
Q4 2.9%
2012
Q1 2.9%
Q2 2.9%
Q3 2.9%
Q4 2.9%
This gives us a forecast for G (2012 economic growth) of 2.9%, and a forecast for Z (number of quarters exceeding 3.6% growth) of 0.
So...
Vp = 47.46 + 0.672*2.9 + 0.990*0
Vp = 47.46 + 1.95
Vp = 49.41
...meaning that Obama would take 49% of the two-party Presidential vote in 2012 -- while the Republican nominee would take 51%.
You can see that on current forecasts, Obama's re-election seems a very close-run thing.
Now, how does "the deal" change matters?
Here I make an assumption: that our growth forecasts had anticipated that the tax cuts and unemployment insurance would be extended, but had not anticipated the payroll tax holiday.
So, what impact will the payroll tax holiday have on economic activity, or GDP?
Mark Zandi estimated to the Senate Finance committee this April that a payroll tax holiday would have a "multiplier effect" of 1.22 -- meaning that for every $1.00 not collected during the holiday, GDP would grow $1.22.
Since the cost of the holiday is $120B, and since the holiday is over at the end of 2011, it would add $149B to 2011 GDP.
Given 2010 Q3 GDP of 14,750B, we have:
GDP GDP GDP GDP GDP
Growth Current added under Growth
Current Forecast under "deal" under
Forecast (billions) "deal" (billions) "deal"
2010 Q3 14,750 14,750
2010 Q4 2.2% 14,830 0 14,830 2.2%
2011 Q1 2.4% 14,919 37 14,956 3.4%
2011 Q2 2.7% 15,018 75 15,093 3.7%
2011 Q3 3.3% 15,141 112 15,253 4.3%
2011 Q4 2.9% 15,249 149 15,398 3.9%
2012 Q1 2.9% 15,359 149 15,508 2.9%
2012 Q2 2.9% 15,469 149 15,618 2.9%
2012 Q3 2.9% 15,580 149 15,729 2.9%
2012 Q4 2.9% 15,692 149 15,841 2.9%
(all growth rates annualized)
As you can see, the payroll tax holiday doesn't add any growth in 2012. So in terms of the Fair model, the value of G remains at 2.9%.
But you'll note that under the payroll tax holiday, growth in 2011 Q2, Q3, and Q4 now exceeds 3.6%. So the value of Z goes from zero to three.
So the Fair model math changes under "the deal":
Vp = 47.46 + 0.672*2.9 + 0.990*3
Vp = 47.46 + 1.95 + 2.97
Vp = 52.38
So if our models and assumptions are correct, "the deal" significantly improves Obama's chances of re-election.
Without it, he takes less than a majority of the 2012 two-party presidential vote: 49% to the Republican nominee's 51%.
With it, he takes more than a majority: 52% to the Republican nominee's 48%.
UPDATE
This diary originally presented results to four significant figures. My thanks to the commenter who pointed out that since the GDP input goes only to two significant figures, the output should not be interpreted to greater precision.