What effect will the debt deal President Obama signed into law on 2 August 2011 have on the projected future level of government spending?
Adding two small data points to Alex Tabarrok's visualization of total federal government spending following the Budget Control Act passage into law, to compare the projects for the next 10 years against the previous ten, and then the previous "pre-financial crisis" ten years:

So, to recap, when compared to the pre-crisis decade of federal government spending, instead of increasing at an annualized rate of 7.35% per year, the total amount of U.S. federal government spending is now projected to only increase at an annualized rate of 6.78% per year, thanks to the so-called "Budget Control Act".
No word yet on whether or not the nation's GDP will grow as quickly....
Data Sources
U.S. White House Office of Management and Budget. Budget of the United States Government: Historical Tables Fiscal Year 2012. Table 1.1 - Summary of Receipts, Outlays, and Surpluses or Deficits (-): 1789-2016. Accessed 3 August 2011.
Congressional Budget Office. The Budget and Economic Outlook: Fiscal Years 2011 to 2021. Accessed 3 August 2011.
U.S. House of Representatives. Text of Budget Control Act Amendment. Accessed 3 August 2011.