WASHINGTON — The Great Recession may be over, but the recovery is just beginning — and it doesn’t promise to be much easier.

Economists forecast the nation’s total output grew at an annual rate of 3.3 percent between July and September, after contracting for a record four straight quarters. That growth has been fueled by a huge influx of government cash, including a temporary tax credit for first-time homeowners and a $1.25 trillion Federal Reserve program to keep mortgage rates low.

Both efforts are likely to end by next summer, and the housing industry is already feeling it. New home sales in September unexpectedly fell 3.6 percent, the first decline since March and a distinct sign of weakness in a market that had rebounded strongly over the summer.

Homebuilders are traditionally big employers, but the industry isn’t hiring yet because there’s a glut of homes on the market. There were 251,000 new homes for sale at the end of September, or about 7.5 months’ supply at the current sales pace. That’s about two months too much.

While the unemployment rate fell slightly in most metro areas in September, the trend was fueled by discouraged job seekers leaving the work force, according to government data released Wednesday.

That may be happening in the manufacturing sector, which has also been pumped up by government building projects. September orders to factories for big-ticket manufactured goods rose 1 percent last month — not a huge increase but an improvement from a 2.6 percent drop in August, the government reported Wednesday. Demand for machinery offset weakness in commercial aircraft and autos.

That report, however, was not enough to distract investors from the disappointing unemployment and housing reports. Stocks fell Wednesday, with the Dow Jones industrial average down 119 points, or 1.2 percent, to 9,805.01.

Shares of homebuilders also tumbled. Hovnanian Enterprises Inc. led the way, falling 3.9 percent, or 41 cents, to $3.89.

Senators agreed Wednesday to extend the tax credit until June 30, as long as buyers sign sales agreements by April 30. Lawmakers were considering adding a credit for homebuyers who already own homes, perhaps allowing up to $6,500 for people who have been in their current home at least five years. Details were still being negotiated.

Critics, however, say many buyers would have made their purchases anyway and call the government incentives an unnecessary subsidy for people who don’t need it. And extending tax credit may have a limited affect, they say.

“Most people who receive the tax credit are people who would have bought a house anyway,” said Ted Gayer, an economist at the Brookings Institution. “That’s a big windfall at taxpayers’ expense.”