PRESIDENT CARTER CAME UP yesterday with a set of important and extremely welcome surprises for the District of Columbia. Based on a taskforce study headed by Vice President Mondale, the administration had pledged its support to a remarkably strong legislative agenda for the city - the most significant presidential move in behalf of the District since the home-rule effort by Lyndon Johnson that eventually led to an elected mayor and city council. If the proposals win the high level of community support they deserve - and if the White House haps Congress, too, will do its part in effecting some long-awaited changes in the way the District is governed.

While it goes without saying that the people of the District have been seeking voting representation in Congress for a good century now, President Carter said much more than that: He went well beyond the general support that the Nixon-Ford administrations gave this effort. Instead of a watery endorsement of some modified form of District representation, Mr. Cater is backing full representation - which today would mean two members in the House and two senators. Legislation approving the necessary constitutional amendment requires a two-thirds vote in each chamber. Whin it a came before the House in the last Congress, a majority, though not two-third, voted approval. Now, with Vice President Mondale, Del, Walter E. Fauntroy and other congressional friends of the city working hard for the measure, it could - and should - get the exposure and understanding it needs. The proposal will need especially strong help in the Senate, where 100 members won't automatically relish the prospect of two more colleagues. Even after successful completion of these steps, the amendment would require ratification by the states.

But as Vice President Mondale said yesterday, "We believe there is no justification for denying citizens equal representation at the federal level because they happen to reside in the District of Columbia."

perhaps the biggest surpise in the presidential package - and one that every taxpayer in the city should cheer - is the White House support for removal of the federal government from the city's local budget process. Congress will not be eager to abdicate its appropriations oversight of a budget that includes a sizeable annual federal payment. But there are many ways in which congressional involvement should be reduced to a minimum. The current system of exhaustive hearings in each chamber - plus an elaborate series of votes including line-by-line scrutiny of the city's requests to spend its own money - needs streamlining, to say the least.

For starters, there is no reason that the budget couldn't be treated in the same manner as any other city bill now enacted by the local government - which brings us to another important change advocated by the administration yesterday. President Carter endorsed a tightening of the time Congress now has in which to review laws enacted by city hall. Currently, Congress has 30 legislative days (an unpredictabe periods) in which it may veto a local bill. The President proposes 60 calendar days, a definite deadline. Moreover, he is supporting elimination of the current presidential review of any bills passed by the city council over vetoes by the mayor.

Other proposals would make additional sensible modifications in the federal control of this city's local business, such as elimination of the silly (and up to now ignored) charter provision establishing a "federal enclave" downtown that is supposed to be overseen by a federal administrator. The White House also is backing an increase in the annual federal payment for $300 million to $317 million for the next fiscal year; and eventually, Mr. Carter would like to see this payment placed under some kind of formula that would permit better financial planning by the city government.

Just as important and welcome is the new presidential support for federal aid in helping the city meet the huge pensions cost s that have accumulated under plans enacted in the past by Congress; for help in cleaning up debts connected with RFK Stadium; for a two-year extension of the city's authority to borrow from the U.S. Treasury until it is able to sell bonds; and for the 1982 transfer of an accredited St. Elizabeths Hospital from federal to local control.

We agree with Vice President Mondale that the White House decision "represent the most progressive steps toward resolving problems in our capital city by any administration in recent years." But the people of this community are understandably wary of lip service. It will be largely up to Mr. Mondale to see that the task-force study as adopted by the President does not suffer the all-too-familiar fate of the governmental commission report; a burst of ballyhoo, followed by a long, slow fade out. In turn, responsible city leaders should do all they can to generate the local support that Congress will be looking for as evidence that people here still want a greater voice in running local affairs - as well as proper participation in the national and international decisions made by members of Congress.