Lower demand resulting from the illustrative policy would decrease real (inflation-adjusted) gross national product (GNP) in 2012, 2013, and 2014 by amounts ranging from roughly 0.1 percent to 0.6 percent depending on the year and the assumptions used. In addition, long-term interest rates would be reduced by about 0.1 to 0.4 percentage points during those years.
Note here that the CBO is basing this off an entirely generic proposal to reduce the deficit by $2 trillion, with no detail as to how that proposal is structured or those savings are achieved: this "lower demand" effect on the economy is just from the general effects of getting that $2 trillion in debt off the books. 0.1 to 0.6 percent reduction in GDP over the next few years doesn't sound like much, but to repeat myself, unemployment is over 9 percent.
In practice the downward pressure could be much more significant, depending on how that $2 trillion was cut. If it is cut by reducing social programs that have a high multiplicative effect on the economy, demand will be cut by that same multiplicative amount. Cut social security, and people buy less things. Cut Medicare or Medicaid, and people have to shift even more of their money to medical expenses.
I don't think there are many people out there arguing that we shouldn't reduce the deficit in the long term, but how you get there obviously matters a great deal. Right now we're still in this strange fetish for austerity that has no rational policy basis, having decided that what we really need to do to get out of a low-demand, high-unemployment situation is to further reduce demand and, what the hell, fire more people. In the states, in the Congress—everyone's agreed, right?
So it seems we simply don't have a choice. Austerity during times of weak economic activity is as ass-backwards as you could hope to get, but no matter: austerity fever is the new cool thing, the policy version of shark attack summer. Stimulus is considered crazy, but cutting government services to the bone in ways that will personally have no effect on the cutters (e.g. do the unemployed really need help? Shouldn't they just use the time to, I don't know, pray for some food or something?) shows your policy seriousness.
It's not even just "austerity," either. It's distinctly one-sided austerity. For the rich, proposing austerity is considered outrageous, and the Republicans have gone to the mat for this notion that the wealthy should not have their taxes raised back up by even one penny—but everyone else needs to have austerity imposed upon them to make up the difference.
Regardless, what the CBO and other policy wonks are telling us is that this newfound austerity fetish isn't going to do a thing to increase short-term demand, but instead is going to further depress it. Which we knew already. But this isn't talked about in polite circles, because the Serious People have decided that high unemployment is just going to be considered the new normal, government isn't going to do a thing about it, and anyone who's not wealthy or incorporated is just going to have to suck it up.