The Democratic National Committee announced a $2 million mid-term campaign effort yesterday, even as President Carter pressed the Senate to provide public financing for next year's congressional races.

Carter promised party leaders over breakfast at the White House that he and his family would campaign for "a strong Democratic showing" in the 1978 election.

An hour later, he used his press conference to plug for Senate action on a congressional public-financing bill, saying "it would help restore the public's confidence and trust" in Congress.

The Senate is scheduled to vote today on a motion to end a Republican filibuster against the bill. With 60 votes needed for cloture, both sides said it is doubtful that Carter could win today but that he is expected to try again later.

Carter and Vice President Mondale have been rallying Democrats to support cloture, with private phone calls as well as Carter's public appeal.

Carter and Mondale early yesterday met officials of the Democratic National Committee and the party's House and Senate Campaign Committees for the first full-scale discussion of 1978 campaign plans.

National Chairman Kenneth B. Curtis said later that "unless there's a crisis in the country," Carter will be "quite generous with his time" in campaigning for Democratic candidates.

Mary Scheckelhoff, the national committee's director of campaign services, said the tentative plan calls for Carter to do half-day swings through groups of states, aiding several Democratic candidates each day. Mondale, she added, will campaign more extensively.

Campaign appearances by Carter, Mondale, Cabinet officials and members of the First Family will be coordinated by Frank Moore, the President's chief liaison with Congress. As Curtis noted, that function "won't hurt" Moore in his efforts to win votes for Carter programs on Capitol Hill.

Curtis outlined for reporters the $2 million campaign plan he presented at the White House meeting. It envisages $1 million of direct contributions to House and Senate candidates and $40.000 for gubernatorial races.

An additional $398,000 will be furnished through in-kind services - polling, research, consultants - for Democratic hopefuls. The remaining will be used for speakers, materials and staff.

The $2-million campaign effort is budgeted on top of the normal $3.25 million Democratic National Committee budget and a $1 million carryover debt from the 1976 campaign, which Curtis hopes to pay off next year.

Curtis said he hopes the Democrats could raise that much for 1978, and announced that Carter will address a party fund-raiser in Los Angeles Oct. 22.

Curtis described the mid-term effort as the "largest" ever undertaken by the Democratic National Committee, but it lacks one feature of a similar campaign the committee managed in 1974.

In that year, then-chairman Robert S. Strauss named then-lame duck Gov. Jimmy Carter of Georgia as chairman of the mid-term campaign committee. Carter traveled around the country, laying the groundwork for his own presidential campaign.

This year, Curtis said with a laugh, "we don't plan to name such a person. "We'll do that in-house."