President Reagan locked horns with House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) in the opening of the 1983 budget battle yesterday and also said that some government employes may now attempt to sabotage his economic program by deliberately making it appear unfair.

Reagan defended himself against Democratic charges that his budget favors the rich. "It is not true that it is balanced on the backs of the needy," the president said of a budget that is $91.5 billion in deficit, not balanced. He also traded public gibes with O'Neill over which of them is more a "country club type."

Among Republicans on Capitol Hill there was more resistance than enthusiasm and Democrats rushed to the offensive against the Reagan budget, predicting that in an election year they will be more successful against the president than they were in 1981.

"It's going to be a more interesting year this year," O'Neill said. "We're going to have a lot of victories this year."

Republican unhappiness was most evident after the two chief budget salesmen in the Cabinet, Treasury Secretary Donald T. Regan and budget director David A. Stockman, held a briefing for all Republican senators who wanted to come. Only about 10 attended, and they emerged to say the budget must be altered.

"I don't think anyone's saying they can live with it," Sen. Malcolm Wallop (R-Wyo.) said. Sen. Rudy Boschwitz (R-Minn.), a member of the Budget Committee, said that there will be compromises and he expects a majority of the committee will want to aim toward a balanced budget in three or four years.

Another committee member, Sen. Dan Quayle (R-Ind.), said Stockman and Regan got the impression "it's going to be tough sledding."

Stockman, who got a taste of the attacks he can expect from Democrats when Sen. Ernest F. Hollings (D-S.C.) called him a "pathological finagler" yesterday, asked the senators for more time before they attempt budget changes.

He told reporters "I'm not going to look for a different mix right now. . . . We'll wait and see what options develop up here." Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) did not attend the briefing, but a Senate leadership aide said he also has been asking for more time by telephoning Senate Republicans to urge them not to abandon the Reagan budget ship "at this point."

Reagan, launching his campaign to win support for the budget as he formally signed copies for transmission to Congress, called his economic program "essential" and promised to stick with it.

He suggested that media stories about hardships caused by his spending reductions should be examined closely. "At times such as these there are those in government employ who will possibly sabotage and deliberately penalize some individual who is not supposed to be penalized in order to get a story indicating the programs are not working," the president told reporters.

The president and the speaker squared off during a 20-minute meeting of bipartisan congressional leaders and Reagan.

O'Neill and House Majority Leader James C. Wright Jr. (D-Tex.) came away incredulous over what O'Neill called one of Reagan's "old hackneyed expressions and stories."

Reagan told them, O'Neill said, of a "woman up in Westchester who makes $75,000 a year and her child is a student on the free lunch program." "Well, I said, 'Mr. President, it can't happen,' " O'Neill said he replied. "I told him I visited my own schools at home. I found that in Massachusetts 640,000 who were given school lunches last year don't qualify this year."

Wright said he thinks someone has misinformed the president if Reagan thinks large numbers of wealthy people have been abusing the school lunch program.

But the president took his first opportunity to keep the debate on the same point. "Do we honestly believe that someone whose parents earn in six figures is entitled to have food stamps because they're going to college? That's what has been going on," he told reporters.

Wright described the Reagan-O'Neill exchange as a "disagreement." He said "you couldn't call it angry."

The disagreement did not keep O'Neill from attending a two-hour White House luncheon in honor of the National Hockey League, but he took up the cudgels upon returning to Capitol Hill by issuing a statement calling Reagan's proposal "a Beverly Hills budget."

That sent the ball back to Reagan's court after a rally over country club contacts that began with O'Neill serving:

"I like the fella. He's got a great personality. He tells a great Irish story, but the truth of the matter is that . . . he has forgotten his roots and he has associated with the country club style . . . . "

Reagan returned: "I know Tip says I associate with the country club crowd. Well, I have only played golf once since I have been president and he is an inveterate golfer and I am sure he must have to go to a country club to play golf."

After O'Neill and Wright made their criticisms to reporters outside the White House, Baker and House Minority Leader Robert H. Michel (R-Ill.) showed up to support the president. Baker insisted that all budgets come under heavy fire just after they are made public.

"I think the president's budget, perhaps with some modifications, is going to be passed," Baker said.

"The Democrats have a big problem because on the one hand they say you ought to spend more and on the other hand they say the deficit is too big," he added.

He said the large deficits predicted by Reagan are going to be politically damaging to Republicans "but I think it is a brave and courageous thing for the president to publish an honest set of numbers." Reagan has said he does not believe any projections beyond one year.

For all his general support of Reagan, Baker in gentle terms said what many Republicans were saying forcibly: that the defense budget should be cut.

Criticism of the budget came from representatives of the "frost belt" as well as the Republican chairman of the National Governors' Conference.

"Our conclusion is that the administration's budget for fiscal 1983 is tilted against the older industrial states of the Northeast and Midwest," the Northeast-Midwest Coalition said.

Vermont Gov. Richard Snelling said the governors' association would oppose the $9.8 billion in cuts for programs administered by state and local governments. "These cuts would fall heavily on many of the nation's most needy citizens and would shift unacceptable burdens to state and local governments already struggling with the recession and deep 1982 federal aid reductions," Snelling said.