WASHINGTON The budding economic recovery isn’t getting much help from the homebuilding industry, which normally creates jobs and drives growth when a recession ends.

Uncertainty over whether there would be an extension of the homebuyer tax credit weighed down construction last month — a sign of how much the fledgling recovery depends on government support.

Homebuilding unexpectedly plunged to its lowest point since April, the Commerce Department said Wednesday. The figures show that builders fear that there aren’t enough buyers to soak up the glut of unsold homes already on the market — a supply magnified by record-high foreclosures.

Congress renewed the homebuyer tax credit earlier this month and broadened its reach. But even with government aid, the weakness of the housing sector is dragging on the economy.

“It will take a while before residential construction begins to contribute meaningfully to growth,” Jennifer Lee, an economist at BMO Capital Markets, wrote in a research note.

The tepid recovery is also holding down inflation. While consumer prices edged up faster than expected in October, they remain lower than they were a year ago. And inflation is expected to stay subdued.

The Labor Department said consumer prices rose by 0.3 percent in October, a bit more than the 0.2 percent that economists had expected. Core inflation, which excludes energy and food, rose by 0.2 percent, compared with expectations for a 0.1 percent rise.

The higher figure was driven by another increase in energy prices and the biggest jump in new-car prices in 28 years. The prices of used cars and trucks also rose by the most since September 1980. Together, new-and used-car prices accounted for 90 percent of the increase in core inflation last month, government analysts said.

Analysts said the jump in used-car prices was due partly to the government’s Cash for Clunkers rebate program. The program reduced the stockpile of used vehicles. This happened because cars that qualified for the clunkers program were junked and so weren’t available for resale.

The clunkers program also drove up new-car prices, analysts said. It helped reduce the supply of new cars just as the latest model-year vehicles, which typically carry a premium, were arriving in showrooms.

“The Cash for Clunkers program may have wiped out the ’09 models that have been sitting there, but the brand-new 2010 models come, and they can command a higher price for those,” said James W. Brock, an economist at Miami University in Oxford,

Ohio, who studies the auto industry.

On Wall Street, stocks edged down after the unexpected drop in home construction and disappointing forecasts from technology companies. The modest drop came a day after major stock indicators closed at 13- month highs, including the Dow Jones industrial average, which has risen on nine of the last 10 days. The Dow dropped by 11 points Wednesday, and the Nasdaq fell by 10 points.

The report on home construction said building of homes and apartments fell by 10.6 percent in October to a seasonally adjusted annual rate of 529,000, from an upwardly revised 592,000 in September. Economists polled by Thomson Reuters had expected a pace of 600,000.

“There has not been much improvement in the underlying demand for new and existing homes,” said Mark Vitner, senior economist with Wells Fargo Securities. “That’s a warning for 2010.”

So is a decline in applications for building permits — a gauge of future activity. Applications fell by 4 percent to an annual rate of 552,000 units. That was the lowest since May and missed analysts’ expectations of 580,000. Still, applications for single-family homes fell by only 0.2 percent.

The National Association of Home Builders said this week that its housing market index remained unchanged in November, reflecting a cautious outlook from home builders. The trade association said its index stood at 17 for the second straight month; readings below 50 indicate negative sentiment.

Developers, facing weak demand and competition from low-priced foreclosures, have scaled back sharply. The number of homes under construction last month fell by 3.4 percent, to 560,000, the lowest on records dating from 1970.

With construction levels low, however, the inventory of unsold homes has been dropping. At September’s sales pace, it would take about 7z months to sell off all the new homes on the market. That’s down from a peak of 11 months last fall. But it’s still short of a healthy level of about a six-month supply.