This chart from Goldman Sachs' Alec Phillips puts the coming era of federal spending cuts in some historical context and you can see that the cuts are big. That's the overlapping impact of the phasing out of the wars in Iraq and Afghanistan, the post-2010 austerity measures forced by the House GOP, and the fade-out of the American Recovery and Reinvestment Act. Note, however, that this is a look at federal consumption and investment—the parts of federal spending that feed directly into GDP—and "transfer payments" on things like Social Security and Medicare are left out.*
When you take state and local spending into account, the spending cuts era has been underway for a while, but state/local also might partially offset this federal trend on a forward-looking basis. California, for example, is back to a balanced budget, and rather than debating what spending to cut, its state legislature will be considering whether some recent cuts can be reversed.
* Update, Feb. 5, 2013: This paragraph was revised to clarify the difference between federal government consumption and investment and overall federal spending.