An attempt to revive the issue of public financing of congressional campaigns failed in the House yesterday, effectively killing the legislation for the rest of the year.

The 213-to-196 vote came on a procedural motion to take up a bill authorizing $8.6 million for the Federal Election Commission. Supporters of public financing had to vote against the motion and send the bill back to the Rules Committee in order to get their public financing proposal to the floor.

The proposal they were backing would have taken effect in the general election of 1980. It would have matched contributions of $100 or less with matching funds from the $1 tax checkoff fund, up to $50,000 per candidate. It was estimated that it would cost about $25 million for the 1980 campaign.

Fred Wertheimer, vice president of Common Cause, the lobby group pushing hardest for public financing, said it was "the closest vote we ever had" on public financing. He said the 17-vote margin was better than the 41-vote margin "in the Watergate year of 1974."

"This keeps the issue alive and we'll be coming back next year," he said. He estimated that the 53 members who are retiring or were defeated in primary elections" voted 2 or 3 to 1" against public financing. "There'll be a huge turnover this year and we'll take the issue to the campaigns," he said.

Actually, public financing came up in March as an amendment to a controversial bill cutting what political parties and fund-raising committees could spend on House races. The House refused, 209 to 198, to even consider that bill. While some argued that public financing killed that measure, Common Cause and other public financing supporters argued it was the unpopularity of the bill with Republicans that killed it.

Supporters demanded that they be given a clean shot at the issue, and yesterday's move was the Democratic leadership's attempt to do that. All members of the Democratic leadership said they support public financing.

Congress voted to publicly finance presidential campaigns in 1974, but has refused - in 1974, 1976 and this year - to extend the financing to congressional campaigns.

Rep. John B. Anderson (R-Ill.), a cosponsor of the proposal, argued yesterday that public financing of presidential campaigns has had the effect of sending special-interest money "flowing in increasing volume into congressional campaigns." Between 1974 and 1976 there was "a quantum leap" in special-interest contributions to House and Senate races from $12.5 million to $22.5 million, he said.

He added that, for the average citizen, public financing was "the best buy around."

Rep. B. F. Sisk (D-Calif.) said, "A vote to spend millions to finance campaigns runs counter to the sentiment of my own state of California on Proposition 13." Rep. Guy Vander Jagt (R-Mich.) said taxpayers who pay congressional salaries would resent being asked to finance getting representatives elected, too.

Rep. Abner J. Mikva (D-Ill.), who said he spent a quarter of a million dollars in his last two, closely contested races, said, "The hardest question to explain is why should it be that expensive. It's wrong and impossible to explain. Public financing is the only way to impose a limit on what's being spent."

Vander Jagt said a spending ceiling would put Republicans at a disadvantage because efforts by labor in the form of workers and get-out-the-vote campaigns - which would not be counted in a spending ceiling - would give Democrats a 2-to-1 advantage.

Rep. Lloyd Meeds (D-Wash.), who is retiring, said he had taken large contributions from special interests in the past, but "I have either felt obligated or ingracious, whether I voted for them or against them. We are being increasingly called upon to put our souls on the line."

The bill authorizing money for the FEC also would prohibit the commission from making random audits of House and Senate candidates' campaign finances.