Despite his advisers' fears that unemployment and economic stagnation could cost the administration its working majority of Republicans and conservative Democrats in the House, President Reagan is convinced that last week's surge in the financial markets is a vote of confidence in the economy.

A senior administration official said today that Republicans, who hold 192 House seats, stand to lose 17 to 25 seats in the general election Nov. 2.

A loss of more than 15 GOP seats, this official added, would jeopardize Reagan's ability to push the rest of his economic program, including further cuts in domestic government spending, through Congress next year. Relatively few of the conservative "Boll Weevil" Democrats who supported most of the president's economic policies appear to be in trouble.

The president and his advisers believe the spending cuts are needed to reduce a budget deficit that they expect to reach at least $160 billion in fiscal 1984.

Nonetheless, Reagan is encouraged by the continued drop in interest rates and the performance of the stock market, which he interprets as a harbinger that the administration's long-promised economic recovery is at hand.

Reagan, who tends inevitably to be optimistic, rewrote portions of a speech on the helicopter ride from Los Angeles to Long Beach last Friday to say that the financial markets were expressing confidence in the economy and to promise to find a job for every American now out of work.

He acknowledged in this speech that September's 10.1 percent unemployment rate announced Friday -- the highest in 42 years -- was "bad news" for the country. But senior administration officials believe they limited the political damage of the new figure by anticipating it, much as they anticipated an "October surprise" that never came during the 1980 presidential campaign.

Today, on the ABC-TV's "This Week with David Brinkley," White House chief of staff James A. Baker III discounted the impact of the unemployment rate on the midterm elections.

"I don't think that the 10.1 percent unemployment figure . . . will be a dramatic event insofar as this election is concerned . . . ," he said. "I do not think it will be a watershed event."

Repeating a statement that is becoming an administration political theme, Baker said that "the 99-plus million Americans who are working are a lot better off than they were two years ago because they've got a lot more by way of purchasing power through lower taxes and lower inflation."

Former vice president Walter F. Mondale, appearing on the same program, said Americans want "a lot less blaming" on the economic issues by both the president and his Democratic critics and some prompt action to ease unemployment and further reduce interest rates.

Mondale urged a $10 billion cut in the defense budget, which Reagan has insisted he will not reduce, and repeal of the third year of the Reagan-sponsored income tax cut for taxpayers earning more than $60,000.

Reagan is committed to continuing the tax cut and said at his last news conference that it would take a "palace coup" to get him to support tax increases in 1983. Today, Baker said "the president would not welcome either higher taxes, additional taxes or acceleration of taxes."

Reagan took Sunday off, sequestered at his mountaintop ranch, 19 miles northwest of here. He will return to the campaign trail Monday when he flies to Dallas for a Republican rally and fund-raising reception for Rep. James M. Collins, the GOP Senate nominee in Texas challenging Democratic Sen. Lloyd Bentsen.

The most important campaigning Reagan is likely to do during the week will occur Wednesday evening in an Oval Office speech officially described by White House deputy press secretary Larry Speakes as a "nonpartisan" report on the economy.

The 20-minute speech is to begin at 7:30 p.m. (EDT), 30 minutes before the scheduled start of a World Series game. White House officials expect the timing of the speech to increase the viewing audience, and they anticipate that Democrats will seek and probably receive free network time for a rebuttal.

Aides said today that Reagan will campaign heavily for Republican candidates in the two weeks before the election. He will begin the first of four two-day political trips Oct. 20 by flying to Peoria, Ill., to speak on behalf of House Minority Leader Robert H. Michel, who faces a serious reelection challenge for the first time in many years.

A White House official said he thinks the resurgent economy is improving Reagan's popularity but doubts there would be "much transfer of the president's popularity" to congressional candidates unless Reagan campaigns for them.