THE HOUSE did well on campaign finance reform Tuesday night. The bill's dogged sponsors, Reps. Christopher Shays and Martin Meehan, the supportive Democratic leadership and the 54 Republicans who broke with their own resisting leadership to vote aye all deserve great credit. The bill now goes to the Senate, where a majority likewise is in favor, but not -- yet -- the 60 needed to break the expected Republican filibuster.

To avert a tie-up of the Senate, the Republican leadership agreed earlier in the year to allow a week's debate on the bill next month, after which there will be a cloture vote. If that fails, the sponsors, John McCain and Russell Feingold, have agreed not to bring up the bill again this year. But next year they can, and the bill's supporters should make clear they will, even at the expense of other business, until the leadership allows the majority to prevail.

The Senate will have no business of comparable importance before it. Mr. McCain has staked his presidential campaign on reform of this system of giving, which he rightly observes is a threat to corrupt all else. The Democrats have their own stake in distancing themselves from the excesses of the 1996 Clinton-Gore campaign, the worst of which this bill would ban. Republicans -- more than the handful who have supported the bill thus far -- likewise have reasons of reputation to vote aye. These mostly moderate members are urged by party leaders to support the current system, because it works in favor of Republicans, who easily raise the most money. Yet they profess to abhor the system for the distorting effect it has on the political and legislative processes. There are ways these members can reduce the conflict between party and supposed principle, but to do that they have to agree to legislate; to filibuster is to toe the party line at principle's expense.

The Senate bill, like the House-passed measure, would bar the use of the national party organizations to raise and spend on behalf of their candidates so-called "soft money," which the candidates are forbidden by law to raise and spend themselves. That was the broadest avenue for circumvention of the law in the last campaign. In its prior form, the bill also sought to limit use of other, ostensibly independent organizations to do the same thing. But opponents call this an infringement of free speech, and the sponsors said yesterday they would drop it to leave no excuse for voting against soft money. Some Democrats have threatened to withdraw their support if that happens. That sort of crossruff has occurred in the past. Democrats, some of whom are themselves uneasy about reform, will support only a bill strong enough that the Republicans can be counted upon to reject it, and the other way around.

First they need to break the filibuster; then they can write a bill.