Washington ? The deal reached by Congress to raise the debt ceiling and cut more than $2 trillion in public spending should have only a minor impact on the economy for the next two years.

Almost all the cuts would be made in 2014 or beyond. The approach heeds a warning by Federal Reserve Chairman Ben Bernanke and many private economists: Cutting too much too soon could harm the weak economic recovery.

Yet the deal won’t do much to help the economy, either, at least in the short term, economists said.

Under the debt deal, discretionary spending, which excludes Social Security, Medicare and Medicaid, would be cut $21 billion in 2012 and $42 billion in 2013, according to an analysis by the Congressional Budget Office.

Combined, those cuts come to less than 1 percent of the nation’s $14 trillion economy. The impact “should be relatively minor,” says Brian Gardner, senior vice president at Keefe, Bruyette and Wood, an investment bank.

The spending cuts would increase to $75 billion in 2015 and $156 billion in 2021, the CBO estimates.

Overall, the first phase of cuts would reduce spending by $917 billion over 10 years. A congressional committee would decide on a second phase of cuts totaling $1.5 trillion.

Reduced government spending could mean less money for highway construction, housing assistance, government-sponsored scientific research or any number of other federal programs.

Companies that work on Defense Department contracts could suffer, too. The stocks of Lockheed Martin Corp., General Dynamics Corp. and Raytheon Co. all sank about 1 percent Monday.

If lawmakers fail to reach a deal on a second round of cuts, the Pentagon’s budget would be cut automatically by about $500 billion. That measure is designed as a threat, to make sure congressional negotiators have strong incentives to compromise.

Delaying the deepest cuts buys time for the economy to recover. Right now, it can’t absorb shocks very well: Unemployment is still 9.2 percent, people are spending less, worker pay has stagnated, and economic growth is the slowest since the end of the recession in June 2009.

Worries about the economy, including the weakest manufacturing in two years, were one reason the stock market couldn’t sustain a rally after the debt deal was struck. The market was flat Monday.

The Federal Reserve meets next week. Economists will watch for any signals that the Fed is considering new steps to help the economy, such as re-investing its government bond holdings indefinitely to keep interest rates down.

The debt deal could restore some confidence among individuals and businesses by removing the fear that the U.S. government would default on its debt for the first time, says Troy Davig, an economist at Barclays Capital.

Overall, the deal could subtract about 0.2 percentage point from economic growth in 2012, Davig estimates. While that is a relatively light blow, the economy only grew at an annual rate of 1.3 percent in April, May and June.