An article in Wednesday's editions of The Washington Post incorrectly referred to a final vote last week in the House Ways and Means Committee in favor of a Democratic alternative to President Reagan's economic program. The vote was in the House Budget Committee; Ways and Means has not yet voted on the plan.

President Reagan slowly working up to a half-day schedule, yesterday received a gloomy private assessment of the legislative prospects for his economic program.

At a meeting with top advisers and his legislative liaison staff, the president was told his program faces tough scrutiny from Democratic liberals in the House and a forceful rear-guard action from Republican conservatives in the Senate.

Three conservative GOP senators deserted the administration last week, causing a 12-to-8 rejection of his economic program by the Senate Budget Committee. The defectors objected on philosophical grounds, saying they could not support the program because it did not provide the balanced budget by 1984 that Reagan has repeatedly promised.

Reagan has instructed budget director David A. Stockman to assure the skeptical senators privately that additional cuts will be forthcoming in 1982 and 1983 to assure a balanced budget. The strategic problem is that the administration wants to reassure the Republicans without tipping its hand to the Democrats.

"We'll just be adding voices to the Democratic chorus of opposition if we outline next year's budget cuts now," one White House source said.

Max L. Friedersdorf, assistant for legislative affairs, told Reagan the administration also faces difficult hurdles in the Democratic-controlled House, where the Ways and Means Committee last week approved a Democratic alternative to the Reagan plan by a 17-to-13 vote.

Friedersdorf said his strategy in the House is to concentrate on a favorable floor vote, targeting "soft Republicans" and some 40 conservative Democrats.

Right now, the outcome in the House is considered too close to call. The White House hopes voters will give members a message of approval for Reagan's economic program during the current Easter recess, but some aides concede this may not be enough to deter the Democrats.

"No one can go home now and say they're for big spending, but that's not what the Democrats are doing," one White House aide said. "They say they're for cutting spending even more than the president."

The White House hopes to counteract this impression with briefings of regional editors by high administration officials. The same strategy was used by Presidents Nixon and Carter in an attempt to build support for their economic proposals. A briefing for 75 editors and reporters from outside Washington will be held today in the Old Executive Office Building and will open with a brief speech by Vice President Bush.

Valuable as these briefings may be, they are considered a poor substitute for Reagan's direct participation in the process of selling his economic plan.

White House officials, some of whom originally hoped to have the president making a radio speech for his program as early as this week, are cautious about predicting a date for Reagan's return as a communicator. The best estimate is that the president will make a televised appeal toward the April 27 end of the congressional recess.

This selling is also likely to take the form of personal telephone calls to key members of Congress -- a type of friendly persuasion Reagan employed frequently before he was shot March 30.

No attempt is being made at this time to rush the president's convalescence.

He is described as napping frequently and eating heartily in an attempt to regain some of the weight he lost while hospitalized.

Yesterday he spent about two hours in meetings with aides. The 30-minute session with his legislative advisers and top aides was held in the Treaty Room on the second floor of the White House.