Obama talked about cutting $2 trillion in spending when he gave a speech a few weeks ago. He has also put cap/trade and some new tax laws into effect for the well off that'll raise $1 trillion over the next decade. Combined with letting the Bush tax cuts expire and Obama will likely get 5 trillion in new revenue or less spending than a GOP president would have done.
And since McCain wanted to stay in Iraq and Obama wants to leave, that could easily save us another trillion or so in lower spending. So I'm guessing Obama's policies will either save or create $6 trillion for the federal government between 2010 and 2020.
Also Obama's healthcare plan is based on ideas from the commonwealth fund, which has said if their ideas are implemented the US would save about $3 trillion in lower healthcare costs over the next decade.
http://www.commonwealthfund.org/Content/Publications/Fund-Reports/2009/Feb/The-Path-to-a-High-Performance-US-Health-System.aspxSo add that in, and add in the savings from Obama's energy policy which will result in lower electric costs, higher MPG cars, cheaper fuels, lower energy needs for autos, businesses and homes, etc. and we will see cheaper energy with less of a need for it.
The way I see it if you add it all together the policies Obama is pushing (the healthcare changes, the tax policy changes, Iraq, energy) Obama is likely going to save the country about $7 trillion in spending on both public/private things while raising an extra $3 trillion in revenue.