President Reagan hopes to use the early months of his second term to galvanize Congress into supporting tax simplification, seek deeper cuts in some federal programs benefiting the middle class and, if possible, renew nuclear weapons talks with the Soviet Union, according to senior White House officials.

The tax simplification idea is a trade-off -- a reduction of tax rates in return for elimination of many existing deductions and exemptions. Reagan said again in a post-victory news conference yesterday that tax simplification "would not result in any individual having his taxes raised by way of a tax reform."

The president will begin his second term with his Cabinet and staff basically intact, officials said, but deputy chief of staff Michael K. Deaver may leave after he directs the inaugural ceremony.

Reagan aides have also privately considered the possible appointment of a special envoy on arms control, but officials said yesterday that it was only "under discussion" and that the president had not yet made a decision. Details, Page A51 .

Hoping to exploit a post-election "window of opportunity" -- a period of six to nine months in which his personal popularity is expected to be high -- Reagan is being urged by White House and congressional advisers to move quickly on a focused agenda of domestic issues and on arms control.

Clashes are always possible, either internally between White House "pragmatists" and conservative hard-liners, or between the lame-duck president and the divided Congress. But Reagan advisers are stressing conciliation instead.

They are considering a cross-country Reagan tour or a series of speeches before the inaugural to build support for tax simplification and bolster Reagan's personal standing before he unveils specific proposals early next year that are certain to be politically costly.

Although major decisions will not be made for several weeks, aides say Reagan is likely to open his second term on these broad fronts:

* Seeking informal congressional agreement on a timetable for trimming the $170 billion deficit by next August. Reagan may try to get the timetable locked in before January during early private meetings with congressional leaders.

* Asking Congress for approval of another round of spending cuts that will hit such politically sensitive programs as military and civilian retirement, Medicare, veterans' health, agriculture, student aid and federal subsidies to business.

* Seeking bipartisan congressional concurrence on a single tax simplification scheme after the Treasury Department finishes its study in December. Although Reagan yesterday reiterated his opposition to a tax increase to deal with the deficit, some of his aides say they think Congress will inevitably pass one, allowing Reagan to reluctantly accept it later, as happened in 1982.

White House officials said Reagan's decisions on budget and tax strategy will be influenced by smaller-than-expected GOP gains in the House. Republicans failed to pick up enough seats to offset the 26-seat loss in 1982, and officials predicted this will make it more difficult for Reagan to put together the winning coalitions he enjoyed in 1981.

"From time to time, we may be able to do it," said one Republican strategist, "but we've got our hands full."

Reagan stopped short of proclaiming a mandate yesterday, and said of the congressional margins, "If need be, we'll take our case to the people."

White House chief of staff James A. Baker III told reporters, "I'm not sitting here claiming a big mandate," adding that any mandate would be determined by "how successful we are in the next four years" in pushing Reagan's programs in Congress.

Reagan's support in the new Congress may be tested first by already scheduled early votes on continuing production of the MX missile, on which the votes were close this year, and on aid to rebels fighting the Sandinista government of Nicaragua, on which this year's margins of opposition were greater, particularly in the Democratic-controlled House.

At the top of Reagan's domestic policy agenda is tax simplification and deficit reduction. The president made tax simplification one of the few specific promises of his campaign, and presidential assistant Richard G. Darman said "we need to move very quickly" to assemble a proposal.

This may take both a public and private track, officials said. The public side may be a nationally televised speech or series of speeches by Reagan, seeking to build support for the idea. The private side would be negotiations with the Congress toward assembling a bipartisan tax simplification plan.

If Reagan does not move quickly on tax simplification, he risks being overwhelmed by opposition from interest groups seeking to protect existing breaks in the tax code, officials said.

Treasury Secretary Donald T. Regan will finish his year-long study of tax simplification in December and is expected to recommend a modified "flat tax," in which many deductions are eliminated from the code in exchange for lower rates.

The current thinking among Republican strategists is that Reagan should take the Treasury study and sit down with the chairmen of the House and Senate tax committees, as well as authors of the major tax revision bills pending in Congress, in hopes of forging a single proposal that could be offered as a "historic, bipartisan plan for tax reform," officials said.

This would embrace two rival proposals, one sponsored by Rep. Jack Kemp (R-N.Y.) and Sen. Robert W. Kasten Jr. (R-Wis.), and the other sponsored by Sen. Bill Bradley (D-N.J.) and Rep. Richard A. Gephardt (D-Mo.)

Most tax simplification proposals are billed as "revenue-neutral," meaning they would not bring in more revenue than the government now receives. But there is a consensus among fiscal analysts, both inside and outside the administration, that a tax increase will probably be necessary as part of any sizable deficit reduction.

A combination of higher spending voted by Congress in September and slower economic growth than anticipated is certain to force the current $174 billion deficit estimate upward when Reagan sits down on Monday for his first meeting on the budget for fiscal 1986.

"My position is solid," Reagan told reporters in Los Angeles yesterday. "We're not going to try and deal with the deficit problem by raising taxes." Reagan said he would attempt to reduce "fat" in government operations through recommendations from a commission headed by industrialist J. Peter Grace.

But administration officials acknowledged that such efforts to trim waste, fraud and abuse have not produced enough savings to bring down the deficit significantly in the past, and cannot be the entire remedy to the deficit next year, either.

There is a difference of opinion among Reagan strategists about how to proceed. Some would like to negotiate deficit reduction with key congressional leaders right away, when Reagan's political clout is at its peak, but others doubt whether that can be done. After a landslide reelection victory, "the last thing Reagan is going to want to do is sit down and negotiate with House Speaker Thomas P. "Tip" O'Neill," said one White House official.

Still, one scenario being discussed is a deal in which Reagan gets spending cuts, in exchange for a temporary tax increase of some kind, devoted exclusively to deficit reduction, that would expire when Congress passes a tax simplification bill, presumably in a year or two. Another scenario is simply a stalemate with Congress over the issue.

Reagan is expected to ask Congress for another round of domestic-spending cuts, particularly in programs that largely escaped the budget knife in his first term. Office of Management and Budget Director David A. Stockman has said that "our biggest failure" in the first term "was that we didn't get a bigger and better package of spending cuts in the beginning," targeted at "the big boulders -- the social-insurance programs."

Reagan has put the biggest "boulder" of all, Social Security, off limits to such cuts. But he is expected to seek reductions in student aid, veterans' health care, medical entitlements, federal military and civilian retirement, federal workers and "special-interest economic subsidies," such as federal aid to build and maintain inland waterways.

Reagan has talked about seeking "reforms" in some of the large entitlement programs, where benefits are distributed automatically to those who qualify. For the most part, aides think he has gone as far as politically possible among these programs that benefit the poor. Instead, Reagan may target those -- like student aid or federal pensions -- that largely benefit middle-class Americans.

Reagan aides also acknowledge that even with new spending cuts, it may be difficult to make significant progress against the deficit without a tax increase, slower growth in the defense budget or a rapidly growing economy.

One option, officials said, would be to adopt optimistic economic assumptions based on the hope that tax simplification would produce an upward "kick" in productivity, and thus more revenue.