President Reagan, reacting to the loss of his working coalition in the House of Representatives in Tuesday's elections, spoke in a conciliatory tone in the White House Rose Garden yesterday about bipartisan compromise with Congress "and a willingness to meet other people's views."

But in a private budget review meeting with his top aides later in the day, Reagan reportedly refused to budge on the key issues of defense spending and tax cuts, which are considered certain to bring him into confrontation with the new Congress in 1983.

"We're not getting anywhere," one administration official confided to colleagues after the meeting.

His comment pinpointed the central but publicly unstated question at the White House in the wake of an election that cost the Republicans far more House incumbents than the administration had expected to lose. As one administration insider put it yesterday, in a parody of the White House campaign slogan, "Is the president willing to change the course?"

Many Californians in the administration have recalled that Reagan proved adept at compromise after being reelected governor of California in 1970. He had no coattails in that election, and Republicans lost the Assembly, the lower house of the California state legislature.

Reagan reacted to that setback with an ambitious legislative program and several compromises with the Democratic leadership that produced a widely acclaimed welfare bill and significant education and tax measures. All of those measures were an amalgam of proposals initiated by Reagan's Republican administration in California and the Democratic legislative majority.

But the present situation may be different, some administration officials have said. While none of them wants to discuss it publicly, they have described the 71-year-old president as being in no mood to retreat from his commitments to a steady increase in the defense budget combined with domestic spending cuts and continuing tax reductions.

Reagan is equally unwilling to seek new revenues to reduce the burgeoning federal budget deficit in 1983. One official, asked yesterday about the possibility of tax increases next year, quoted the president's statement at a September news conference that it would require "a palace coup" for him to agree to this.

A senior administration official responded yesterday to a question as to whether Reagan would agree to pare his original projections for the 1984-85 defense budget by saying: "I do not see him as having changed now. And if you ask me what I think he's going to do, I don't think he's going to change."

This official ruled out compromises with Congress before the administration submits its budget. He said it is "not unlikely or impossible that there could be such a compromise solution" after the budget is submitted.

Some within the administration believe Reagan will lose his opportunity for compromise unless he signals early that he is genuinely willing to accept alternative proposals. These officials anticipate that Democrats will be emboldened by their success in the midterm elections and that a number of Republicans will join them, at least in an attempt to scale back military budget increases.

A cheerful Reagan, answering questions for 14 minutes in the sunlight of the Rose Garden, did not seem to share any of these worries.

The president claimed that the average loss in midterm elections "in times of economic stress" was 46 seats. Reagan ignored the more commonly used barometer of the first midterm test for a party that captured the White House in the previous election. This average loss, since World War II, is 11 seats. Republicans lost 26 House seats Tuesday.

"We feel very good about what has happened," the president said.

But others doubted whether the administration could survive any more such victories. Before the election, administration officials had drawn up varying scenarios of what would happen in the election.

The worst case involved a loss of 27 seats but only 19 Republican incumbents. All of the 26 losers were GOP incumbents, a key statistic since most of these Republicans were replaced by liberal Democrats unlikely to support Reagan economic programs.

Officially, the White House continued to display the optimism exhibited by Chief of Staff James A. Baker III Tuesday night when he called the election results "a wash."

Using words almost identical to Baker's, the senior official said that "from time to time on selected issues we'll be able to pull the conservative coalition together . . . on selected issues."

But the mathematics on which this premise is based requires a creative definition of "conservative Democrats."

In seeking to prove that the makings of a conservative coalition remain intact in the House, administration officials counted every Democrat who had voted with the president on a key economic bill, including some who cast consistent anti-administration votes in 1981. By doing this, the administration came up with a figure of 77 "helpful Democrats," including 65 who won reelection.

The White House numerical exercise counts these 65, another 15 Sunbelt Democrats elected Tuesday and the 165 Republicans in a pool of 245 "from which we can draw in trying to continue to preserve the coalition in the House," the official said.

The total of House members counted by the White House as real members of the coalition tell a different story. This figure, not used for public consumption, listed 45 Democrats as coalition members on the basis of fairly consistent support of administration economic programs. Of these "Boll Weevil" Democrats, 42 are back.

Adding this total to the 165 Republicans -- some of them moderate-liberal "Gypsy Moths" who do not always vote with the coalition -- gives a total of 207 members, short of the 218 needed for a majority.

Estimates outside the administration are that only two or three of the newly elected Democrats are likely to join the conservative coalition.

It is doubtful whether the president is aware of the gloomier private estimates of congressional prospects in 1983. For all of his skill at political communication, Reagan is rarely interested in this sort of detail and remains, according to one White House source, "unquenchably optimistic" for the success of his policies.

On election night, according to Baker, Reagan was "upbeat." White House spokesman Larry M. Speakes said yesterday that the president went to bed at 11:51 p.m., not bothering to wait for returns from his home state of California, where the victories of gubernatorial candidate George Deukmejian and Senate candidate Pete Wilson provided two of the happiest moments of the evening for Republicans.