The House Democratic leadership is making a last-minute effort to get Congress to approve partial public financing of next year's House elections.

This morning, the House Administration Committee will attempt to mark up a bill with an eye to getting it on the House floor before adjournment.

Although public financing of the 1976 presidential election has met with almost unanimous approval, pressure for carrying the system on to Congress had faded.

The Senate dropped a proposal for public financing of its elections earlier this year in the face of the firm Republican and conservative Democratic opposition. In the past the Senate has approved such measures.

Traditionally, the House has been opposed to public financing of its elections. The large number of House races, opponents have claimed, would make it an administrative nightmare. There is also underlying opposition from incumbents who believe they would get tougher election day opponents if there were a guarantee of adequate campaign funds.

The current push on public financing came from the Democratic Study group. Some 155 members asked Speaker Thomas P. O'Neill Jr. (D-Mass.) and House Administration Chairman Frank Thompson Jr., (D-N.J.) to move onthe measure, which has been tied up since the spring.

Adding impetus to the request was defeat of the cargo preference bill where campaign contributions from maritime unions and shipping interests had helped stimulate opposition to the measure.

As drafted by the committee staff, federal funds would be available only to major party candidates in House general elections.

They would have to raise $10,000 in contributions of $100 or less for their first federal aid, which would be a free districtwide mailing, rather than cash.

Thereafter, every contribution of $100 or less would be matched by federal funds up to a total of $25,000.

A candidate could continue to raise campaign funds but they would not be matched. Furthermore, any candidate accepting the federal funds could only spend a total of $150,000 on his or her race - including the free mailing which would be valued at $25,000.

If one candidate exceeded that limit, the opponent could also spend more - and receive further matching funds up to another $50,000.

Problems are expected to develop early during today's markup and according to informed sources, there is some doubt that a bill can be drafted before Congress adjourns.

For example, there is expected to be controversy over the initial threshhold figure as well as the inevitable problems over third party and independent candidates.

Proponents of public financing want the system opened to all prospective candidates, not just those of major parties. Other fears that the easy availability of federal campaign money would encourage interest groups - like those favoring abortion or gun control which can easily raise threshhold money - to enter single issue candidates.