A bipartisan group of senators who led the 1974 post-Watergate fight for total federal funding of all congressional elections plan to introduce a more modest bill Monday to provide only partial funding of Senate primary and general elections beginning in 1978.

On the House side of the Capitol, another bipartisan group is at work hammering out an even more limited federal funding program that would cover just the general - and not the primary - election of representatives.

Both congressional efforts got a booslt last Wednesday when President Carter said during a press conference that he supports the idea of federal financing of House and Senate elections.

Carter said Vice President Mondale would draw up an administration proposal to cover all congressional races. Senate aides said, however, they expect Mondale will only endorse the public financing concept.

President have left to Congress the drafting of laws that involve the election of House and Senate members.

In both houses, the bills being drafted will emphasize matching funds with continued private contributions rather than the provision of total federal financing. That is one change from the 1974 bill that passed the Senate. Another is that each body will develop its own separate system. Both moves reflect hard political and campaign finance lessons learned over the past two years.

Last year's total federal financing of the presidential election caused unhappiness because of the elimination of private contributors. At the same time the matching fund system employed in the presidential primaries worked well - and is the basic element in the bill, prepared by Sen. Dick Clark (D-Iowa), Sen. Edward M. Kennedy (D-Mass), Sen. Charles McC. Mathias (R-Md.:, Sen. Richard S. Schweiker (R-Pa.) and Sen. Alan Cranston (D-Calif).

Strong House opposition in the past to any federal funding plan for its elections led the drafters to limit their plan to the Senate.

The bill would provide federal dollars to match each contributions of $100 or less to a Senate primary candidate.

To qualify, a candidate would have to raise on his own a "threshhold" amount that would be set at 5 per cent of the overall spending limit for his state. In no case would that be less than $15,000 in small states, nor more than $50,000 in larger states.

In general elections, the major party candidates would receive an initial block grant equal to one-quarter of the spending limit. Then for each private contribution of $100 or less, they would again receive matching funds up to the state's spending limit.

Third party and independent Senate candidates would be entitled to matching funds once they had privately raised a "threshhold" fund equal to one-quarter of the spending limit.

The bill does not require candidates to accept federal funds. But once they did they would be bound by the spending limits.

The House bill, as now planned, will provide federal matching funds to House candidates in general elections for contributions of $100 or less. The matching funds, however, would be available only up to the first $50,000 raised. Therefter, a candidate would have to raise funds entirely on his own.

The House bill would put a $150,000 spending limit on any candidate that accepts the matching federal funds.

Third-party candidates would also be eligible for matching funds but the House drafters have not worked out how they would qualify.

House primaries would not be covered by the program.

A special escalator provision has been drafted in the Senate bill to handle what is known as the Hinz situation. In last year's Pennsylvania Senate race, H. J. Heinz III used some $2.5 million of his own money in winning both the Republican primary and the general election. His opponents were unable to compete with him because of fund-raising limitations.

To handle this situation, a candidate taking federal funds under the new bill would not be held to the spending limits if his opponent, using private money, spent more. In that situation, matching federal funds would still be available if the publicly financed candidate wanted to continue raising and spending funds in competition with his richer opponent.

The new bill also sets higher overall spending limits than existed for last year's presidental campaign. Thus, in primaries, the limit would be established at 15 cents per eligible voter, while the general election limit would be 20 cents.

A Senate candidate running in Pennsylvania, for example, would be permitted to spend about $1.6 million in the general election. Heinz, according to Federal Election Commission reports, spent about $1.8 million.

The bill drafters set high, rather than low, spending limits to quiet those critics who complained in the past that challengers to incumbents have to spend more in order to win.

Clark, according to a Senate aide, hopes to have Rules Committee hearings on the measure by late March to permit passage sometime this year. The Iowa Democrat, who is up for reelection next year, would like to have the bill become law before his campaign begins.

The measure will not have amendments to the presidential election law attached, though several are expected to be added during the Rules Committee consideration.