IT WAS FITTING that the bill for public financing of House campaigns was beaten in committee the other day by a coalition of Democrats who wanted less competition and Republicans who wanted more. Some of the Democratic nay-sayers apparently feared that public financing would undercut their old-line organizations and fuel GOP challenges. Many of the panel's Republicans, who tend to regard public financing as a Democratic plot, concluded that most elements of the plan, especially its limits on campaign spending, would help incumbents and hurt challengers.

The contradictions here illustrate the clashing interests that the advocates of public financing have never managed to overcome. They have tried hard for several years to devise a plan with something for everyone-or at least a majority. The point of general appeal has been the possibility of relief from importuning interest groups and the grubbier aspects of campaign fund-raising. But most House members have also insisted on protecting their own political alliances and advantages. In response to various concerns, the bill kept being tinkered with. Finally it became as complex and assailable as the "system" it was meant to supplant.

In short, the bill was probably beaten less by any one opposing force, such as Republicans or corporate interests, than the sheer variety of the situations it threatened to disturb. That is appropriate, because public subsidies of House general elections, and spending limits, and the exceptions to those limits, and all the rest would alter politics in many districts in ways that would not be entirely predictable-and probably, in some respects, regrettable.

For all the weight of those uncertainties, there is a stronger argument against trying to advance a public-financing bill this year. That is the certainty that the Federal Election Commission could not manage it. The commission is going to be hard-pressed enough by the 1980 presidential campaigns. Piling on the responsibility for policing public subsidies and spending limits in several hundred congressional campaigns is a sure way to immobilize the agency, or the campaigns, or everybody in a hopeless snarl.

All in all, partly for the wrong reasons, the House committee came out in the right place. For now, those who want to improve campaigns should concentrate on straightening out the FEC. If that doesn't consume their energies, they could look for simpler ways to give some start-up aid to congressional challengers and reduce the leverage that political action committees can apply.