The Reagan administration began its drive yesterday to sell a skeptical Congress on the wisdom of the president's fiscal 1983 budget and the $91.5 billion deficit it would entail, a deficit that both Democrats and Republicans on Capitol Hill see as a threat to recovery from the current recession.

Yet there was also talk yesterday by White House aides and congressional Democrats of taking a major step that would almost certainly add to the deficit: speeding up this summer's large scheduled tax cut to help the economy revive.

On the budget generally, White House counselor Edwin Meese III advised doubters yesterday: "Never underestimate this president's ability to mobilize the American people behind his policies." President Reagan leaves today for a series of speeches in Minneapolis, Des Moines and Indianapolis, designed to sell his budget and the companion program to turn more than 40 federal programs over to the states.

But he leaves with warnings in his ear that his effort to increase Pentagon spending by nearly a fifth while cutting all but a few basic domestic programs almost as much will face considerable opposition in this election year, not just from affected interest groups and congressional Democrats, but also from key Republicans as well.

"The Republicans I talk to . . . are frightened about the deficits," said Senate Finance Committee Chairman Robert J. Dole (R-Kan.), who at the same time predicted tough sledding for Reagan's proposals to trim food stamps and other domestic spending. "I don't think we can tolerate a $92 billion deficit, and that's an optimistic figure."

"The president's budget will be difficult to pass in its entirety," said House Minority Leader Robert H. Michel (R-Ill.). Rep. Barber B. Conable Jr. (N.Y.), ranking Republican on the House Ways and Means Committee, cast doubt on the prospects for the half-dozen small tax increases Reagan proposed. He said he does not agree with the basic premise behind the proposed minimum tax on corporations, that the proposed 5 percent withholding on interest and dividends won't get out of the starting gates and that the entire tax proposal could become a vehicle for Democratic "mischief."

But Meese and David A. Stockman, the director of the Office of Management and Budget, took an upbeat tone in television appearances. Meese, a guest on "This Week with David Brinkley" (ABC, WJLA), said, "The president still has strong support in the country. People still like his programs. They feel that with his programs, we will be better off in the future."

And Stockman, appearing on "Face the Nation" (CBS, WDVM), said that "as Congress looks at the hard, stark choices available, they will understand very quickly that unless measures of the magnitude that we have proposed by way of savings are adopted, that then there could well be a severe threat to the economic recovery."

Stockman and Meese both ruled out major cuts in the defense budget or a delay in the third year of the scheduled tax cuts, measures urged by many Democrats on Capitol Hill.

But Meese opened the door to a different proposition, making the 10 percent rate cut now scheduled for July 1 retroactive to Jan. 1. That move--designed to pump new consumer spending and savings into the sluggish economy--is something the administration "would want to look at very carefully," Meese said.

If it were not linked to a plan to delay or cancel the final 10 percent cut scheduled for mid-1983--as many Democrats have proposed-- "I think we would not have much objection to that," he added.

Sen. Bill Bradley (D-N.J.), a member of the Senate Finance Committee, suggested on "Meet the Press" (NBC, WRC) that the tax cut be advanced from July 1 to April 1.

House Budget Committee Chairman James R. Jones (D-Okla.), one of those advocating postponement of the 1983 cut, said accelerating this year's reduction "has some appeal to it if it lowers interest rates." He said the timetable for action in the next two months was "very difficult, but it is an option we're going to consider very carefully."

As Reagan leaves for his first sales trip on the new budget, there were reports that the weekend meeting of his senior staff members and political advisers at Camp David produced a consensus that he faced a difficult and perhaps uphill battle to repeat his 1981 budget and tax victories on Capitol Hill.

"We're looking at a very rough year unless there's a fairly strong and visible economic recovery by the second quarter April-June ," one participant said, in summarizing the mood of the meeting.

The pollsters and political advisers who met with the top White House aides were reported to have said that Republican chances in the November elections were no less dependent on a spring recovery than the budget program. "The key to success is recovery by May or early June without the return of high interest rates," one adviser said.

Stockman, the battle-scarred budget chief who faces his first congressional interrogations on the new budget this week, said the business and financial world would look to Capitol Hill for reassurance that the Reagan economies would be accepted.

"To some substantial degree," he said, "the burden will be up there to determine whether we can make the same kind of headway this year in paring back the size of government and the size of the budget that we did last year." Stockman predicted that Reagan would come "pretty close" to last year's record, when "we got more than 80 percent of what we proposed."

Asked if he was setting the stage for blaming Congress for any deficits higher than Reagan projected, the budget director said, "I don't think we should be in the business at this early point before the ink is even dried on the budget of casting blame, or casting praise. What I'm saying is that these . . . huge budget savings are necessary, essential to keep the economic recovery program moving forward. And I think that those on the Hill who have a chance to look at it will recognize that's precisely what we have to do."

But House Budget Chairman Jones, who said Stockman's figures were off base, told reporters, "I'm just frankly tired of the scapegoat business" in which he said the administration was engaged.

Like many others, he argued that the budget cuts were either unrealistic or undesirable.

There is clear opposition to many of Reagan's proposals from an array of powerful groups that would lose benefits or see their taxes rise. They range from universities through stockbrokers and bankers, governors, government retirees, boat owners and defense contractors to the aviation and nuclear power industries. The administration says it has moved in the budget to reduce the deficit $55.9 billion below what it otherwise would be under current law. At least a third of these reductions already have identifiable interest-group opposition.

For example, lobbyists for the universities were beginning as early as last month to mobilize students, professors, parents and alumni to fight cuts in the college student grant and loan programs. Reagan has proposed cutting these popular programs by $800 million in the next fiscal year.

Reagan would raise $12.7 billion with a number of relatively minor and technical tax increases. Developers, aerospace companies and weapons producers have already signaled opposition to one of these, which would raise $3.3 billion by accelerating the rate at which they must pay taxes. The president's plans for raising $1.1 billion by closing a tax loophole advantageous to the insurance industry has also provoked strong reaction.

The U.S. League of Savings Associations, bankers and stockbrokers have for years battled successfully against the proposal in the budget for raising $2 billion by requiring that taxes be withheld from dividend and interest payments.

The president's plan for raising $2.5 billion through various user fees is similar to one he advanced last year that was defeated after vigorous lobbying by airplane and boat owners and other affected groups.

Governors and mayors who have complained for months about the extent of spending reductions they sustained in the first round of cuts have since late last year repeatedly announced their intention to fight further reductions. The president has proposed shrinking spending by about $10 billion for federal grant-in-aid programs to state and local governments and the entitlement programs they oversee.

For the states and local governments, the opposition is likely to be particularly intense since the administration in its plans for a "New Federalism" has agreed to freeze spending over the next several years for many of their programs at the levels set in the 1983 budget.

Other portions of the budget likely to be controversial include the plans for saving about $1 billion by changing the way cost of living adjustments are made for civilian and military government retirees; reducing hospital reimbursements under Medicare by 2 percent and reducing or eliminating compensation for veterans who are partially disabled.