The administration's plans to press for new budget cuts of $10 billion to $13 billion are creating significant dissension within the ranks of the House Republican leadership as some key GOP congressmen voice fears that the administration is demonstrating panic instead of confidence.

At the same time, the Democratic House leadership, after absorbing two major defeats on the budget and tax bills, has adopted a conscious policy of avoiding direct confrontation with the Reagan administration. "We want people to look at the economy, not some political fight between Tip House Speaker Thomas P. O'Neill Jr. and Reagan," one aide said.

The contrasting attitudes within the two political camps reflect an extraordinary shift in the atmosphere on Capitol Hill as Republicans are on the defensive for the first time since the start of the 97th Congress and Democrats have gained a slight edge of confidence.

This shift has developed as Republicans have become increasingly fearful that high interest rates not only will damage the administration's economic program but their own political futures as well; and Democrats are in the position for the first time this session where they can watch the GOP squirm over the failure of Wall Street to rebound after passage of the budget and tax bills.

At a meeting of the House GOP leadership yesterday morning, at least two members -- Richard B. Cheney (R-Wyo.), chairman of the policy committee, and Barber B. Conable Jr. (R-N.Y.), ranking member of the Ways and Means Committee -- questioned the strategy of seeking new, and politically painful, budget cuts.

"I felt it doesn't make any sense at all to suddenly make changes in a program that hasn't even gone into effect yet," Cheney said after the GOP meeting. Other sources at the closed session said he was particularly critical of administration officials conducting what amounted to a public debate on television since the middle of August over the need to make new cuts in order to pacify Wall Street, to lower interest rates and to patch up the crumbling bond market.

On a similar tack, Conable, referring both to administration officials and to some congressional colleagues, said "I think there are too many people panicking . . . The president's program hasn't taken effect yet. It doesn't serve our purposes or our country by rushing around trying to do something to add to the turmoil."

The GOP leadership, however, is split on strategy. Rep. Robert Michel (R-Ill.), the minority leader, for example, strongly supports new budget cuts as a method to demonstrate the firmness of the commitment to austerity, and he has gone so far as to suggest that Congress may back credit controls if interest rates remain at current levels exceeding 20 percent.

According to sources, Michel's support of additional cuts was backed up by Rep. Delbert L. Latta (R-Ohio), a proponent of major surgery on government spending.

Privately, however, some Republican leaders -- including those firmly in the conservative camp -- are voicing concern that the Reagan administration is placing excessive emphasis on achieving the target of a $42.5 billion deficit in 1982.

"They are too hung up on the $42.5 billion number," one Republican said. "If you come in with a budget deficit bigger than $42.5 billion , well, what the hell, it's the long-term trends that count and we've achieved that."

In addition, these Republicans contend that the administration's efforts either to turn the appropriations process into a major battle or to seek powers of impounding money appropriated by Congress only serves to demonstrate a lack of confidence that the program as now passed is adequate.

They noted that one of the major problems during the Carter administration was continued changes in economic policy, many of which took place under circumstances very similar to the present. In March 1980, for example, the Carter administration and Democratic leaders made a sudden, and futile, decision to try to balance the budget when the inflation rate hit 18 percent and the bond market was falling apart. The unsuccessful effort only served to decrease public confidence in the administration.

Concern over high interest rates also is growing among Democrats who backed the administration on the budget or tax bills, or both.

Rep. Elliott Levitas (D-Ga.), who deeply angered the Democratic leadership by supporting the administration's three-year tax bill, said yesterday that the problem of high interest rates is "a real political -- not time bomb -- but atomic bomb that is ticking right now. If interest rates don't come down, all the other business about economic recovery goes out the window."

In an effort to avoid turning the economic problems into a partisan conflict that the Reagan administration could turn to its advantage, O'Neill told Democratic leaders yesterday that he intends to carefully avoid the spotlight, including appearances on television.

He and a number of other Democratic leaders are calculating that many of the cuts in federal programs go into effect on the first of next month, which will result in public attention not only on economic conditions but also on the consequences of the reductions.

Conable, thinking along similar lines but from an entirely different vantage point, noted that the Oct. 1 effective date on the cuts will make it all the more difficult for the Reagan administration to win passage of new reductions and pointed out that a political failure in Congress could weaken public confidence in his economic program.