President Carter proposed yesterday a far-reaching and comprehensive plan for increased home rule in the District of Columbia including full voting representation of two senators and two representatives in Congress and budget autonomy for the city's elected government.

The long-awaited proposals announced by Vice President Mondale, chairman of a special 14-member White House task force on District of Columbia problems, formed one of the strongest presidential commitments ever to D.C. self-determination, according to several observers.

"I am proud of the decisions that have been made," Mondale said. "I believe they represent the most progressive steps taken toward resolving problems of our capital city by any administration in recent years."

City leaders were in near unanimous agreement with the Vice President.

"They've attempted to address not only representation but also the expansion of human rights in many ways that have never been addressed by a President before," said Mayor Walter E. Washington.

In addition to full voting representation - which would give the city two senators and two representatives in the House instead of the present single nonvoting House delegate - the White House proposed removal of many of the federal checks on local autonomy that were included in the 1974 Home Rule Charter.

These included recommendations to abolish a so-called federal enclave, established to protect the welfare of federal property in the District, removal of the President's current review authority over some city legislation, a streamlining of the process by which Congress reviews all city legistation and, within five year, budget autonomy for the city government from Congress and the administration.

In addition, Carter asked for the commitment of federal funds to help bail the city out of some of its most weighty fiscal problems, including unfunded pension liabilities of more than $2 billion and $20 million in outstanding loans for the Robert F. Kennedy Stadium.

The White House urged the federal government to pay half of the $20 million RFK debt and a total of 12 per cent of the costs of a plan that would result in full funding of the outstanding pension liabilities in 25 years.

The President's proposals were the first step toward expanded home rule, but many of the key items suggested face numerous major obstacles before they are realized.

Full voting representation, for example, must be approved by a two - thirds majority vote of both houses of Congress, since it takes the form of an amendment to the Constitution, it must be ratified by 37 of the 50 state legislatures. One observer predicted that that total process of voting on this is Congress and the state would take at least four years.

An equally steep uphill fight is expected on the issue of budget autonomy, which is strongly desired by the city's elected officials, but jealously guarded by key members of the congressional committees that presently have oversight on the city's financial affairs.

In addition, the president's recommendation in an of itself does not guarantee passage of any legislation by Congress. The crucial factor, in the view of many Washington observers, is how forcefully the White House will lobby for favorable congressional action.

James Dyke, an aide to Mondale, said yesterday that no decisions have yet been made by the Cater administration on tactics.

"We're going to have to talk to our congressional liaison people first. I can't say now what form that support will take," Dyke said. "But I think the fact that the President has said he strongly supports it should reflect his strong commitment to get things done."

A bill to permit full voting representation in Congress fell 45 votes short of passage in the House last year.

"The President is worth at least 45 votes. It ought to be a piece of cake in the House if we all do our jobs and the President puts his weight behind it," said Council Chairman Sterling Tucker.

Del. Walter E. Fauntry (D.D.C.) said yesterday that he plans to meet this week with the House leadership in an attempt to schedule a floor vote on full-voting legislation now before a congressional subcommittee before Congress goes on vacation next month.

Fauntroy said he hopes to achieve House passage then and concentrate all efforts next year on what is e task of approval in the Senate.

Some senators are expected to resist the dilution of their influence that would result from expanding that body from 100 to 102 members. Others are known to feel that only states should be represented in the Senate. The pending measure does not grant statehood to the District.

A major sticking point in granting full budgetary autonomy to the city is the need to set the level of the annual federal payment, which compensates the city for the loss of revenues on untaxed federal properties.

That amount is now established after the two congressional appropriations committees review the city budget item by item, as they do with federal departments.

Existing law sets the maximum payment at $300 million, but the actual amount to be granted by COngress for the 1978 fiscal year - which starts Oct. 1 - seems sure to be less than that figure. Carter endorsed a $317 million authorization yesterday for fiscal 1979, the sum the mayor has requested.

City officials have long pushed for an automatic payment of a predetermined amout. A congressional committee began exploring a method to establish a formula last year. but the question was dropped when Cogressadjourned. It has not been revived.

When Congress enacted the District's home rule charter in 1974. Rep. William H. Natcher (D-Ky.), the influential chairman of the House District Appropriations Subcommittee, insisted upon continued budgetary control as his price for supporting the new governmental setup. Natcher is known not to have changed that position.

Nevertheless, some leading city officials are privately hopeful that by the time the proposed transition to full budge autonomy is completed in 1982, Natcher may have moved on to the chairmanship of a more prestigious subcommittee. Natcher could not be reached for comment yesterday.

The pension fund assistance is regared by city officials as one of the most urgent matters to be resolved. The city has no established fund to pay more than $2 billion it owes in future benefits to police, fire fighters, teachers and judges. The pension programs were mandated by Congress.

Legislation scheduled for House action next Monday would grant nearly $800 million over the next quarter century, a sum equal to 20 per cent of the anticipated payments during that time into the pension funds. The White House's Office of Management and Budget recommended last May that the federal aid be cut to $400 million. or 10 per cent. Carter raised the figure yesterday to 12 per cent, or nearly $500 million.

Chairman Charles C. Diggs Jr. (D-Mich.) of the House District Committee and other key members told a press conference yesterday that they will continue to push for their more generous funding.

The home rule charter presently gives the President authority to review locally passed legislation in instances where the City Council has overridden a veto by the mayor. President Carter asked that such review authority be abolished.

"The people of this city should not be subjected to burdensome and wasteful executive review procedures in matters that involve no significant federal interest whatsoever," Mondale said.

Carter also asked for a streamlining of the present congressional review period. which requires all city legistation to undergo a review period of 30 days during which both Houses are in session. Because of frequent congressional recesses, that time frame is unpredictable and sometimes takes several months. Carter proposed instead a specific number of calendar days, such as 60.

The White House also proposed that St. Elizabeths Hospital, the federally run Southeast Washington facility for mentally retarded persons. be transferred to the District by 1982. During the intervening five years, the federal government would work to regain the facility's accreditation and would phase out its financial support after 1982.

Polly Shackleton. chairman of the City Council's committee on human resources. said that even if the facility were accredited, the city would need federal money to run it. The hospital's annual budget is about $80 million.

The President also recommended a two-year extension of the city's current authority to borrow money from the Treasury Department to finance capital improvement projects. The politically more sticky issue of a tax on suburban commuters working in the city was left for further discussion by the task force.