The index of leading indicators, which signals future changes in the economy, fell for the ninth straight month in January, indicating that the end of the recession is still not in sight, the Commerce Department reported yesterday.

Deputy Treasury Secretary R. T. McNamar candidly acknowledged yesterday that the economy is still declining and that unemployment "may yet go to 10 percent before we get things turned around." The unemployment rate fell from 8.8 percent in December to 8.5 percent in January, but most analysts expect the February figure to go up again when it is reported Friday.

At the White House, President Reagan told reporters the recession "has begun to level out. That always happens at the bottom. You've got to have a curve before you turn up." [Details, Page A8]

The president's optimism on the economic outlook apparently has strengthened his determination not to give in to congressional demands that he postpone the scheduled 10 percent tax cut for individuals in 1983 as well as making other budget changes.

The index of leading indicators, which usually gives advance warning of economic turning points by two months or more, fell 0.6 percent in January. An increase of 0.6 percent originally reported for December was also revised to show a 0.3 percent decline.

But the drop in the January index would have been much larger if Commerce Department economists had not decided to omit the influence of one indicator--the length of the average workweek--which dropped precipitously that month partly because of severe winter weather across the nation.

If the average workweek had been included, the entire index would have dropped 2.8 percent for the month, the department said. A Commerce spokesman said the workweek indicator would also be omitted from the February index to avoid the distortion of a weather-related rebound.

Commerce Secretary Malcolm Baldrige said the continuing decline in the index means "that the recession has yet to run its course."

Baldrige said, however, that the drop in the index in each of the last three months was smaller than those earlier last fall, and added, "The fact that the indicators were on the minus side in January is not inconsistent with forecasts of a second quarter recovery in the economy."

Baldrige, in a statement, said he was particularly encouraged by recently falling short-term interest rates, since "the actual course of [economic] activity will be heavily influenced by the trend of interest rates."

Increases in interest rates in December and January are thought by many economists to have delayed the recovery.

Meanwhile, economist Alan Greenspan told the Senate Budget Committee that the decline in consumer spending and industrial production seems to have slowed in February. At the same time, he said, "there is very little in the way of strength evident in materials orders."

Greenspan said that a second "early indicator of an upturn . . . is a rise in the number of workers being rehired relative to those being laid off. There is no evidence yet of this occurring. Thus," he concluded, "while the evidence suggests the rate of decline is slowing and, in fact, we may have hit bottom, indications of an upturn are scant at best."

Jack Carlson, chief economist of the National Association of Realtors, was less sanguine. Carlson said the January drop in leading indicators indicates the current recession will last at least six months more. "It is apparent that high interest rates are cutting into orders for plants and equipment and that so long as investment in these areas is lacking, unemployment will remain high and economic recovery will be hampered."

The biggest negative factors included in the January index were declines in new orders for consumer goods and materials and in stock prices.

Other indicators showing poorer records for the month were contracts and orders for new plants and equipment, total liquid assets, prices for sensitive raw materials and average weekly initial claims for unemployment insurance.

Three indicators showed better performance: A growing money supply, building permits and delivery performance.

Separately, the Commerce Department said spending for construction fell 1.5 percent in January to a seasonally adjusted annual rate of $231 billion. That level was 10.8 percent below the same month last year and 16.4 percent lower when inflation is taken into account, the department said.

The Labor Department, meanwhile, said that productivity of non-farm businesses did not decline quite as much in the fourth quarter of last year as originally reported. Revised figures show that output per hour worked fell at a 6.8 percent annual rate instead of the 7.6 percent rate originally reported.

Despite the decline in the fourth quarter, and a 1.8 percent rate of decline in the third, productivity for 1981 as a whole was up 0.9 percent, the first gain in four years.