The nation's unemployment rate rose to 10.8 percent in November, the highest level since the spring of 1941, as 12 million Americans looked for work and could not find it, the Labor Department reported yesterday.

Moreover, details of the bleak pre-Christmas report gave no hint that the economic recovery so long promised by government and private forecasters alike is near. Several economists said the unemployment rate now seems certain to pass 11 percent even if the recovery does begin before long.

Virtually every industry continued to lay off workers last month, helping boost the jobless rate from 10.4 percent in October. Employment dropped in all but three of 22 goods-producing industries and in three of five service industries, the department said.

In several large industrial states, the seasonally adjusted unemployment rate rose by close to a full percentage point. In Michigan the rate climbed from 16.1 percent to 17.2 percent, a Depression-era figure equal to the national average in 1939.

Administration economists, like their private counterparts, generally expect a recovery to begin soon, certainly before the middle of 1983. But they were not expecting such bad news on the unemployment front for November.

"Yes, it is a lagging indicator," said economist Allen Sinai of Data Resources Inc., an economic consulting firm. "But when the figures are so high, it says something. It casts a shadow over a recovery."

The shadow falls directly on the prospects for consumer spending in the Christmas season and beyond, along with residential construction, the only sector of the economy in a position to spark an economic rebound.

"With so many people out of work and others afraid of losing their jobs, [consumer] demand is not yet picking up," declared Jerry Jasinowski, chief economist of the National Association of Manufacturers. "With industrial production declining and interest rates still much too high, the economy is caught in a vicious cycle of declining output, declining employment and declining demand."

Added Donald Strazheim of Wharton Econometric Forecasting Associates, "There really are just no bright spots at all. When you look at various industries, employment is down in almost every instance, and that was true in October as well. If November were the trough of the cycle, the figures should have been mixed. Instead, they were universally bad."

Post-Depression unemployment records were set last month virtually across the board, the Labor Department said. The jobless rate for adult men rose from 9.8 percent to 10.1 percent, that for adult women from 8.6 percent to 9.1 percent, and that for teen-agers from 24 percent to 24.2 percent, all records.

The unemployment rate for whites also reached a record 9.7 percent, up from 9.3 percent in October. The rate for workers of Hispanic origin rose 0.5 percentage points to 15.7 percent, a new high. The rate for blacks remained at 20.2 percent, a record, for the third month in a row.

The 440,000 jump in the number of unemployed workers is certain to intensify the political struggle in Congress over bills that are supposed to create new jobs.

Many economists maintain that neither Democratic jobs programs nor the separate $5 billion highway and bridge repair bill backed by the administration and most members of Congress would create any noticeable overall increase in the number of jobs, particularly if the costs are offset by higher taxes. For instance, one economist, Albert Wojnilower of the First Boston Corp., yesterday labeled such programs "smaller than peanuts."

Janet L. Norwood, commissioner of labor statistics, told the Joint Economic Committee, "As the recession continues, the number of unemployed who have been out of work for long periods increases. In November, 38 percent of the unemployed had been jobless for 15 weeks or longer; more than half of these had been out of work for more than six months.

"It is also important to remember that people are continuing to enter the unemployment stream," she continued. "Four million unemployed persons in November had been jobless less than five weeks."

Of the 10.8 percent of all workers who are unemployed, 6.7 percentage points represent those who lost their last job. And, 2.3 percentage points was accounted for by persons reentering the labor force, 1.1 percentage points by persons seeking their first job, and only 0.7 percentage points by persons who voluntarily left their last job.

The Labor Department also reported that the index of aggregate weekly hours worked in goods-producing industries fell 1.7 percent in November, a strong indication that industrial production also declined for the month.

At the same time, the high level of joblessness continues to hold down wage gains. The hourly earnings index for production and non-supervisory workers on private non-farm payrolls rose only 5.5 percent in the 12 months ended in November and is up at only about a 3 percent annual rate in the last three months.