WASHINGTON – Unemployment claims, already well into recession territory, are rising even faster than expected, leading economists to warn Thursday that the worst is yet to come.

As the Labor Department released bleak new numbers on the job market, Goldman Sachs, Chrysler and Xerox all announced they were cutting workers by the thousands, adding to the woes of an economy beset by tighter credit and wobbly banks.

The government said new applications for unemployment insurance rose 15,000 last week to a seasonally adjusted 478,000, above analysts’ estimates of 470,000. Jobless claims above 400,000 are considered a sign of recession.

The White House, in unusually stark language, acknowledged the economy is going through what spokeswoman Dana Perino called a “rough ride.”

“We expect our GDP [gross domestic product] number next week not to be a good one and the next quarter to be tough as well,” Perino said.

The Commerce Department will release its first estimate of third-quarter economic performance Oct. 30, and Wall Street analysts project it will show the economy contracted by 0.5 percent, according to Thomson-IFR.

Many economists expect the decline to continue into the current quarter and the first three months of 2009, if not longer. The classic definition of a recession is at least two consecutive quarters of negative growth.

Former Federal Reserve Chairman Alan Greenspan, testifying before a House committee, said he could not see “how we can avoid a significant rise in layoffs and unemployment.”

Zach Pandl, an economist at Barclays Capital, estimates that unemployment will rise to between 7 percent and 8 percent by early next year. Other economists have estimated it could rise to 8.5 percent.

Currently, the unemployment rate is 6.1 percent. Unemployment peaked at 6.3 percent in 2003 after the brief recession of 2001. It peaked at 7.8 percent in the 1991-92 recession and above 10 percent in 1982.

Maine’s unemployment rate rose slightly in September from 5.5 percent to 5.6 percent. An estimated 39,800 Mainers were unemployed last month.

Last year at this time, the state’s unemployment rate was 4.9 percent.

The Goldman Sachs Group Inc. said it would cut about 3,260 jobs, or 10 percent of its work force, in the face of what Greenspan called a “once-in-a-century credit tsunami” that has claimed several of Goldman’s rival investment banks.

Chrysler LLC said Thursday it would cut 1,825 jobs, and Xerox Corp. said it plans to eliminate 3,000 positions, or 5 percent of its work force.

Other companies have announced reductions this week: Yahoo Inc. is cutting 10 percent of its employees, or 1,500 people; drugmaker Merck & Co. is eliminating 7,200 positions; and financial services firm National City Corp. will shed 4,000 jobs.

The impact of the job losses is rippling through the economy. As jobs disappear, foreclosures rise when out-of-work homeowners can no longer make mortgage payments.

Home foreclosure filings jumped by 70 percent in the third quarter, according to the listing service RealtyTrac Inc. Nationwide, nearly 766,000 homes received at least one foreclosure-related notice from July through September, the company said.

Greenspan said that in order for the financial crisis to end, home prices must stabilize. But he said that was not likely to occur for “many months in the future.”

Spending is falling, too. Americans who still have jobs are worried about keeping them, and those who have lost jobs must watch every penny. Consumer spending accounts for about 70 percent of the economy, and economists estimate it fell by more than 3 percent last quarter in what would be the first quarterly drop in 17 years.

Democrats in Congress have urged that unemployment benefits, which last for 26 weeks, be extended as part of a new economic stimulus package. Democratic presidential nominee Sen. Barack Obama endorsed that plan in a statement Thursday and said he would also “suspend the taxes on those benefits and jump-start job creation by giving small businesses emergency loans and tax credits for each new job they create.”

His Republican opponent, Sen. John McCain, said he would “make sure that bailout dollars are used to … stop the foreclosures and free-fall in housing prices.”

“Times are tough, and we need immediate action to take this economy in a new direction,” he said in a statement.

The four-week average of jobless claims, which smooths out fluctuations, dropped slightly last week from a seven-year high to 480,250, the Labor Department said.

The number of people continuing to claim unemployment insurance dropped by 6,000 to a seasonally adjusted 3.72 million, down from 3.73 million, a five-year high.

Claims were also higher because of the impact of Hurricane Ike in Texas, the department said, which added about 12,000 requests for unemployment benefits, the same as the previous week.