The 96th Congress -- an offspring of Proposition 13 and a national mood that has persuaded elected politicians to proclaim that less is better -- convenes Monday determined to define a new politics of austerity.

"I would guess the mood would be to go the president one better in his well-advertised insistence on a tight budget," said Rep. Jim Wright (E-Tes.), the House majority leader. "The impulse will be to call him and raise him" in cutting spending, Wright said. Other House and Senate leaders agreed.

But beyond this overriding theme, congressional leaders are reluctant to make many specific predictions for the 96th. Nearly a fifth of the new Congress is newly elected, continuing the pattern of rapid turnover of recent years. The 96th Congress convenes at a time of uncertain conditions at home and abroad and under a president whose politicl influence two years before the next election remains erratic.

A downturn in the nation's economy could overcome today's budget-cutting fever, members of the House say, and a full-fledged recession could lead to a renewal of old-fashioned pump priming in the form of tax cuts and increased federal spending.

However, members in both houses and both parties agreed in interviews last week that initially, the push for austerity is likely to dominate domestic issues. In the Senate, a great debate on an expected strategic arms limitation treaty (SALT) with the Soviet Union will also be a major event, and may consume many weeks of the Senate's time.

Leaders in both houses predicted that these other issues would be important this year:

A new general trade agreement with the other industrial nations, which will set protectionist sentiments in Congress against the administration's free-trade policies.

Legislation that would permit the United States to maintain the essential elements of its old state-to-state relations with Taiwan now that Washington has recognized the People's Republic of China. This legislation will allow opponents of the recognition of Peking to vent their disapproval.

Legislation to control health costs, particularly in hospitals, which failed in the last Congress. Passage of hospital cost containment might be followed by consideration of limited national health insurance.

Legislation to implement the controversial Panama Canal treaties that the Senate approved last year. This bill could provoke a serious fight, particularly in the House.

Reorganization legislation, including a measure to create a Department of Education and possible realignment of programs now within the Commerce and Housing and Urban Development departments.

Trucking deregulation.

Leaders in both houses also said the 96th Congress will spend more time this year on "oversight" -- heraings and investigations into the operations of federal programs.

Rep. John Brademas (D.-Ind.), the House whip, said Congress would turn to oversight activities instead of "writing a lot of new legislation." Oversight gives Congress something to do, and could also provide reasons for cutting various programs.

Along with this new interest in oversight, many in Congress are sympathetic to "sunset" legislation, which provides for the automatic termination of spending programs agter a fixed period of timne unless both houses reauthorize them. The Senate passed a sunset bill last year.

Members of both houses also have expressed interest in finding ways to reduce government regulations, particularly those that might contribute to inflation. Business lobbies have seized on the popularity of this idea as a way to pressfor changes in regulations they find especially onerous -- for example, the governnent's clean air standards.

President Carter's ability to influence this Congress is a subject of speculation as the House and Senate reassemble after a three-month adjournment. In the absence of Senate and House members, Washington's attention has focused on the administration's budget-making process, but on Capitol Hill it seems unlikely that whatever Carter sends up in his budget will wurvive congressional scrutiny.

Despite Carter's series of end-of-session victories in the last Congress, doubts persist about the durability of the partnership between the White House and the Congress, dominated by large democratic majorities.

Majority Leader Wright noted, for example, that although the administration has been making important -- if tentative -- policy decisions all fall, "There has been no meeting of congressional leaders with the president since early October." Wright said the president "still hasn't learned to consult congressional leaders" before announcing controversial policies.

As an example. Wright cited the disenchantment of House Ways and Means Committee Chairman Al Ullman (D-Ore.) with "real wage insurance," the administration's proposal for rebating some taxes to organized workers who accept pay raises that fall within the President's inflation guidelines. The Ways and Means Committee plans to open hearings on this idea on Jan. 29.

If the President had called congressional leaders and Ullman in, Wright said, "perhaps we could have modified it in such a way that he (Ullman) could have supported it."

As it is, this proposal -- the only element of Carter's fight against inflation that will be considered by Congress -- faces serious opposition in Ways and Means. Moreover, it will provide a vehicle for eager tax- and spending-cutters in the House to offer as a substitute one or more of their personal schemes for imposing more austerity that could embarrass the administration early in the new Congress.

One idea that might fall into this category is to index the tax code to inflation, a proposal backed by Republicans in both houses and an apparently increasing number of Democrats, too.

The sponsors of various tax-cutting plans, including the Republican-supported Kemp-Roth legislation, promise to bring their ideas up again this year.

"I used to think this year would be easier" than 1978, one administration lobbyist observed last week, "but now it looks like it will be just as bad as last year."

Electoral politics are likely to contribute to the administration's difficulties. For example, the Republicans will be preparing for the 1980 presidential elections, and several wouldbe candidates in the Senate will be polishing their presidential images. If Cater's political standing remains relatively poor, Republicans probably will be increasingly eager to take him on.

In the Senate, this could mean less cooperation for the administration from Howard H. Baker Jr. (R-Tenn.), the minority leader. A senior administration lobbyist predicted that Baker would be more independent this year, partly because he is considerin a presidential run. An aide to Baker added that the senator is unlikely to forget how Carter came to Tennessee last fall to campaign for Baker's opponent.

The Senate as a whole will be more conservative this year, partly because of the Novermber election results, and partly because of members' perceptions of the national political mood.

"There's a stampede away from the traditional Democratic approaches" to domestic issues, according to an aide to Edward M. Kennedy (D-Mass.), one of the few senators to remain unabashedly liberal.

Of the 34 senators up for reelection in 1980, 24 are Democrats, 13 of them liberals. Colleagues expect many of the Democrats to be looking for more conservative positions this year as they begin preparing for reelection campaigns.

In the House, Republican gains were modest -- 11 seats. But as House Minority Leader John Rhodes (R-Ariz.) said, "There were all those Democrats who campaigned as bornagain conservatives... They'll have plenty of opportunity to put their votes where their campaign rhetoric was."

Rhodes predicted that Republicans will win some of the budget-reduction fights that they lost last year by close margins.

In both the House and Senate, enthusiasm for self-regulation of member' ethics appears to e waning despite well-publicized transgressions of members from each body. In the Senate there has been alk of abolishing the special ethics committee, in part because there does not appear to be a single member who wants to serve on the panel this year.

The House is also having trouble filling seats on its ethics committee.

However, neither body can avoid dealing with pending cases, especially those of Rep. Charles C. Diggs Jr. (DMich.), and already-convictd member who could become the first person expelled from Congress since 1860, and Sen. Herman E. Talmadge (D-Ga.), who faces formal inquiry by the Senate Ethiecs Committee.

As in th last congress, sinle-interest groups are expected to be a powerful force. They proably will continue to opeate only in ehalf of their pet objectivs, and "there is no cohesion, except on the fringes," in the words of Rep. Richard Bolling (D-Mo.), likely the new chairman of the House Rules Committee.

Members agree that turmoil in the world and uncertainty about the domestic economy could limit the value of any predictions about the course of the 96th Congress.