President Reagan's special envoy on the Lebanon crisis reported yesterday that the situation has cooled, thanks to the 4 1/2-month-old cease-fire.

Ambassador Philip Habib, who just returned from the Middle East, said the risk of the Lebanese tensions blowing up into a major confrontation remains, but that every party to the dispute had expressed interest in maintaining the cease-fire, which Habib helped arrange July 24.

"I found during my visit, and I so told the president, a general desirability that Lebanon should not be the center of either military or political upheaval that would create problems throughout the region," Habib told reporters as he left the White House after meeting with Reagan.

Habib said, in response to a question, that Syria, which strongly opposes the Camp David peace process and whose troops occupy much of Lebanon, desires to maintain the cease-fire. He did not mention other parties by name, but Israel, the Israeli-backed Christian forces in southern Lebanon, the Lebanese government and the Palestine Liberation Organization are all involved.

The United States does not deal directly with the PLO, but Habib said the parties had indicated their positions to him "one way or another."

Habib said he had no plans to return to the Middle East, but would respond to any new request from Reagan.

In another development at the White House, Reagan was visited by Rep. Jack Kemp (N.Y.) and nine other Republican House members who ardently support his tax-cut program. The delegation urged him to make a new demonstration of his faith in the economic doctrine that holds that tax cuts will stimulate the economy.

They asked Reagan to advance the date his tax cuts take effect from July 1 to Jan. 1. Deputy press secretary Larry Speakes said that Reagan would consider the request, but that Treasury Secretary Donald T. Regan had cautioned that it would be difficult to get such legislation through Congress in time to have significant impact.

Kemp told reporters he had suggested to the president, "Why not lower the tax rates in January and get us out of the recession earlier?" A 5 percent reduction took effect Oct. 1 and a 10 percent cut is due July 1.

It appeared, however, that, while Reagan wants to give polite consideration to the suggestion from some of his most devoted allies in the House, he would prefer not to change course at this late date, when he is a month away from a new struggle with Congress over the 1983 budget.

Reagan initially proposed larger tax cuts taking effect earlier than Congress approved, but Speakes said that Reagan wants to "remain on target, to remain consistent."

Former president Gerald R. Ford also visited Reagan and emerged to say that because of the recession the GOP would not do well if an election were held in the next two months. Ford predicted, however, that the economy will start improving by summer and will be considerably stronger by November's elections.

"All the economists with whom I've talked tell me that, by the end of the spring, early summer, the economy will start to move forward, interest rates will be down, the rate of inflation will be significantly less and unemployment will be trending downward," Ford said.