The House Administration Committee yesterday soundly defeated a bill to provide partial public financing of House election campaigns, virtually killing the measure.

In my judgment it is probably dead for this Congress," House Administration Committee Chairman Frank Thompson (D-N.J.) said after the 17-to-8 vote. Eight Democrats voted against the bill despite strong pleas from House Speaker Thomas P. (Tip) O'Neill Jr. to support it. They were joined by all nine committee Republcians.

Supporters of public financing in the House Democratic Study Group and Common Cause, a public Advocacy lobby, immediately said they would seek to have the House Rules Committee bring the bill to the floor. This has happened three times in the past six years, after the House Administration Committee killed the measure.

But Speaker O'Neill and Rules Committee Chairman Richard Bolling (D-Mo.) were cool to the idea, despite the fact that they are both strong supporters of public financing.

Asked if he would urge the Rules Committee to bring public financing to the floor for a vote, O'Neill said, "No, it's a bad precedent." But he added that if the Rules Committee took the action on its own, he would not object.

Bolling said he would not want to "take the time of the House unless it's going to pass." He described House members as "quaking aspens" in the face of controversial bills this year and indicated he doubted they would vote for public financing.

But Fred Wertheimer, Common Cause vice president, said a vote in the House would be "very close" and contended the House deserved the right to vote on the issue.

Supporters of public financing said the vote in the House Administration Committee was much closer than the final tally indicated, and that several Democrats would have supported the bill if they could have gotten the last one or two votes needed to put it over.

O'Neill personally appealed to Rep. Joseph G. Minish (D-N.J.), one of the swing votes, to support the bill, but failed to change his mind.

Thompson blamed the bill's defeat on "terrific heat from strong Democratic organizations," such as the Cook County machine in Illinois and party organizations in Pennsylvania and New Jersey.

Deputy Whip Dan Rostenkowski (D-Ill.), an important figure in the Cook County machine, which fears a loss of influence if public financing is adopted, opposed other House leaders and lobbied committee members such as Frank Annunzio (D-Ill.) hard to oppose the bill.

Richard Conlon, Democratic Study Group staff director, also blamed "vicious" lobbying by the Chamber of Commerce and business groups that have formed political action committees to contribute to House and Senate campaigns.

Special-interest contributions to House and Senate races have skyrocketed by 370 percent in the last six years, from $8.5 million in 1972 to over $32 million in the 1978 election.

Public financing is necessary to stop special-interest buying of influence in Congress, it supporters say. Most of the money goes to incumbents, and many veteran Democrats oppose public financing, fearing it would finance challengers.

Under the bill, contributions of $100 or less would be matched up to $60,000 with federal funds for general election races. Eighty percent of the funds would have to be raised in a candidate's own state. In return, a candidate would accept a spending limit of about $200,000 for his or her campaign.

Most Republicans oppose the spending limits, saying the ceilings favor incumbents, whom they claim have an unfair advantage of free mailings, allowances, staff and other perquisites.

Rep. David A. Stockman (R-Mich.) co-sponsored the bill, then voted against it in the House Administration Committe yesterday because he said he objected to spending limits.

A former supporter of public financing, Rep. Charles Rose (D-N.C.), voted against the bill this year because he said he objected to using taxpayer money to finance campaigns. Others said business groups and the Chamber of Commerce put pressure on Rose, but he denied it.