First, Federal spending is a component of GDP, which measures the output of the entire economy. For more, see Discretionary Fiscal Policy. Second, higher income taxes take money out of consumers' pockets. Higher business taxes are either passed on through higher prices, or reduce funds companies have to hire workers or invest in new projects. For more, see Supply-side Economics
What could happen specifically? First is sequestration, a mandatory 10% Federal budget cut occurring in FY 2013. It was created by Congress and the President to resolve the 2011 debt crisis. Second, is arguments over the FY 2013 budget and raising the debt ceiling, both of which must be approved by April. Long-term, it means a reduction in the three largest budget items: Social Security, Medicare and military spending.
As Washington wrestles with the best way to go about this, it creates uncertainty about tax rates, benefits and federal programs. Businesses react to this uncertainty by hoarding cash, hiring temporary instead of full-time workers, and delaying major investments. Don't expect a robust recovery until the debt-to-GDP ratio is closer to the benchmark 90% level. It was 103% at the end of 2012.
The Federal Reserve assumes that sequestration is avoided. It forecasts GDP growth improving to somewhere between 2.3% to 3% in 2013, and accelerating to somewhere between 3% and 3.5% in 2014. It will stay at that same level (between 3% and 3.7%) in 2015, and settle into a slower 2.3% to 2.5% range after that. (Source: FOMC Committee, Economic Projections of Federal Reserve Board Members and Bank Presidents, December 2012)
However, the Fed is slightly more optimistic in the short run. It forecasts unemployment dropping slightly in 2013, somewhere between 7.4% and 7.7%. The rate will further drop in 2014 to somewhere between 6.8% and 7.3%. In 2015, the rate will drop even further, within a range of 6% and 6.6%. (Source: FOMC Committee, Economic Projections of Federal Reserve Board Members and Bank Presidents, December 2012)
The $16 trillion debt means that the U.S. really can't afford to wage large ground wars anymore. The successful raid to eliminate Osama bin Laden showed that special ops are more cost-effective. In the FY 2012 budget, security spending (including Homeland Security, Overseas Wars and Veterans Administration) reached a peak of $895 billion -- more than either Social Security or Medicare. This was projected to shrink to a low of $749 billion by FY 2015, which will help the budget deficit drop to $610 billion that year. (Source: FY 2013 Federal Budget, Summary Tables, Table S-5: Proposed Budget by Category)
To avoid losing value in their dollar holdings, foreign investors are diversifying their portfolios with more non-dollar denominated assets -- even the euro. Result? Higher import prices, contributing to inflation, as well as lower export prices, spurring economic growth. However, the good news is that is will be a gradual dollar decline, not a dollar collapse.
Bernanke based this on how former Fed Chair Paul Volcker ended the stagflation of the 1970s. By keeping interest rates high, it reassured the public it was committed to preventing inflation.
The only hiccup to this rebound will be in 2015, when the Fed uses reverses quantitative easing and a zero-bound Fed funds rate. As mortgage rates rise, housing prices will drop to offset the higher cost to homebuyers. Hopefully this will only be enough to prevent another asset bubble, but not enough to dry up demand.