There are two parts to the debt ceiling compromise: (1) is a decrease of about $900 billion in the Federal budget over the next 10 yrs.; (2) is an additional cut in the Federal Budget of $1.1 trillion over the next 10 yrs (I have seen the figure quoted as high a $1.5 trillion) to be decided upon by 12 congressmen over the next six months. In addition, Part 2 has a "poison pill" proviso in it that, if a Super Committee of 12 congress people cannot come to a recommendation of how the $1.1 trillion of cuts can be made, then there is an automatic decrease in the budget of $1.1 trillion with half coming from defense and half from discretionary spending. If the Super Committee can come up with a compromise, then it will be immediately voted on, without amendments, by congress. I can't see these 6 Republicans and 6 Democrats coming to a compromise so I presume that the "poison pill" proviso will occur.
Steven Rattner made an interesting discussion of this on Morning Joe on August 3rd (http://www.msnbc.msn.com/id/3036789//vp/44000516#44000516). Rattner shows a graph in which are shown the increase in the Federal budget before and after the Part 1 of the debt limit compromise. In 2020 he estimates that the Federal Budget would be 25.9% of GDP, whereas the increase in Federal revenues will be only 18.4% of the GDP. Part 1 of the debt limit compromise, however, will reduce the increase of the Federal budget to 24.4% of GDP, lowering the rate of increase in the Federal Budget so it is approximately parallel to the rate of increase of revenues, and thus shows an annual Federal Deficit to $1.5 trillion, presumably in perpetuity.
Rattner did not consider Part 2 of the debt limit compromise because it hasn't been enacted yet, but, if the poison pill is enacted, the projected deficit in the Federal deficit should be in a gradual decline as percent of GDP with a slow convergence to the Federal revenues.
As might be expected, "defense" hawks in congress object to the provision in the "poison pill" that 50% of the cuts come from the DoD and claim it will ruin our security. No doubt this is overstated as they only need to cut $55 billion from a continuous program from a budget in excess of $671 billion for 2012 to come to $550 billion over 10 yrs. The cuts from discretionary spending are a little more severe in a discretionary budget of about $500 billion in that they would have to cut $55 billion from continuous programs to arrive at the $550 billion, their contribution. There are Departments and Administrations with much larger budgets than this. For example the the Presidents proposed discretionary budget for the Department of Education Budget for 2012 is $77,400,391,000 which is reduced to $66,023,391,000 by a decrease in mandatory funding. Though there are those that propose shutting down the Department of Education, it is unlikely to occur. Some other departments with budgets above $55 billion/year are: Agriculture, Health & Human Services, Treasury, Office of Personal Management, and Social Security Administration. I don't suppose that any of these budgets would be totally or significantly reduced. For example in Agriculture, congress hasn't even been able to get themselves to eliminate the corn-based ethanol subsidy, even though the savings in carbon dioxide emission are marginal, and, if you cut down a forest to grow corn, you come out behind.* Not only is the corn based ethanol subsidy marginal in reducing carbon dioxide, but fields converted to corn from other crops help make these other crops more expensive.
Because Step 1 of the Debt Ceiling Compromise only slows the growth of the Federal Budget, I assume it will not push us into a recession,** but , if Step 2 is invoked, the Federal budget will begin to go negative and detract from our GDP (Gross Domestic Product) along with our negative Net Trade Balance. Both Government spending and the Net Trade Balance are in the equation to calculate the GDP. The net Trade Balance deficit right now is around $500 billion a year so would be $5 trillion dollars over 10 years (If the economy improves, it will be greater, and, if we go into a recession, it could be less.). Though it is only a guess, Step 2 might subtract an additional $2 trillion from the GDP over the 10 years. My reasoning is that if $900 billion decreases the rate of increase about in half, another $900 billion should flatten the rate of increase and allow another $200 billion (to make a total of 1.1 trillion) to start decreasing the Federal budget. As the consumer is pretty well tapped out, it will be left to industry to make up for the estimated $7 trillion from the negative Net Trade Balance plus the decrease in the Federal Budget and to push us into a positive GDP. There is no way we can have a positive Net Trade Balance because we refuse to face up to our addiction to foreign oil. Unfortunately, this addiction also leads us to fund our enemies to fight us. I have no idea if companies can more than make up for the negative estimated $7 trillion contribution to GDP from the Net Trade Balance plus the decrease in the Federal spending.
* Note added January 5, 2012. Toward the end of December of 2011, the subsidy was in fact repealed; however, the tariff and percent of gasoline that must be ethanol has not changed and in fact was increased from 10% to 15% by Obama (http://247wallst.com/2011/12/30/us-ethanol-subsidy-is-history-adm-vlo-peix-gpre-czz-rds-a/ & http://www.nytimes.com/2010/10/14/business/energy-environment/14ethanol.html).
**Actually, whether the $900 billion of Part 1 can put us into a recession is complex because the deductions are back loaded, i.e. they will be more in the out years than the near years over the 10 years. I don't know by how much the back loading is. If, say, $500 billion were to be taken out in any one year, it could push us into a recession, but the back loading is probably not that severe. The same applies to Part 2, but is more serious as the Federal budget actually is reduced.