
This graph supposedly compares "Democratic Budgets" and the Republican Alternative based on spending as a percentage of GDP between 1980 and 2080. As you can see, Democratic spending is, as they say, off the charts after about 2060.
Now I think it's perfectly fine for Paul Ryan and the House Budget Committee's Republican staff to make whatever crazy assumptions they want about Democratic spending. No one has to take them seriously. But I don't think they can say that this is "based on CBO's Long-Term Alternative Fiscal Scenario" unless the CBO has actually done an analysis that runs through 2080. As far as I can tell, the Congressional Budget Office hasn't done any such analysis. But they have scored the Obama budget through 2019, and it looks like this:

As near as I can tell, Paul Ryan and his staff just took the CBO projections that ended in 2019 and drew a random line, extending upward at about a 45 degree angle, until 2080. There's no real attempt to make it look scientific.










Why don't you put in a call to Ryan's office and ask them about the graph?
What would Republicans do if Democrats actually deigned to let the relevant committees hold hearings on the alternative budget and Ryan et al's accountants had to defend their projections under oath and explain their qualifications?
I'm curious what the projected GDP is in Ryan's budget. It's suspiciously absent.
Try http://www.cbo.gov/doc.cfm?index=9216. Table 2 matches the graph relatively well. It puts spending as percent of GDP at 75% in 2080, with 40% going to paying interest on the national debt.
The first link hit from googling "cbo long term" is cbo.gov/ftpdocs/88xx/doc8877/12-13-LTBO.pdf - long-term CBO budget projections from 2007. However, since the cite is "based on," it's not clear what, if any, changes Ryan staff made to the CBO numbers.
The link Talbot referes to has this to say about the revenue side of the deficit projection:
In December 2007, the Congressional Budget Office (CBO) published The Long-Term Budget Outlook, which presented a long-term projection of the budget under an "alternative fiscal scenario," representing one interpretation of what continuing today’s underlying fiscal policy would mean. CBO projected that, under that scenario, spending on Medicare, Medicaid, and Social Security would rise rapidly, and federal outlays excluding interest (primary spending) would climb from about 18 percent of GDP in 2007 to 28 percent in 2050 and to 35 percent in 2082 (see Table 1). Because the scenario also assumes that revenues as a share of GDP would not increase much over the 75-year period, CBO projected that the federal budget deficit and federal debt held by the public would rise sharply.
So, there is no forecast of revenue beyong a naive forecast and health care reform doesn't happen. Medicare and Medicaid go from 4.1% of GDP to 19.3%. Interest expense thus grows from 1.7% to 40.1%. This deficit projection has nothing to do with Obama's budget and everything to do with the current health care system.