SEVEN TIMES last summer Senate Majority Leader Robert Byrd tried to break a three-month-long Republican filibuster against a bill to reform the squalid system of congressional campaign finance. Seven times he failed; a majority favored the bill, but not the 60 needed for cloture. Now Mr. Byrd has indicated he is going to try again in an election year, and good for him.

He has two targets: the moderate Republicans so fond of being seen -- often with cause -- as among the constructive swing votes in the Senate, and Minority Leader Robert Dole. Three of the sensible Republicans stepped across the party line on the bill last year -- Robert Stafford of Vermont, John Chafee of Rhode Island and, on the final cloture vote, Nancy Kassebaum of Kansas. The first two were among the legislation's cosponsors. Mrs. Kassebaum reserved the right to vote against it but did not want to be locked in the same room with the present system either. The moderates could cut a deal with the sponsoring Democrats and quite likely improve the bill in the process; they should try.

Mr. Dole should too. His involvement arises partly from his presidential candidacy, a theme of which is his (demonstrated) legislative leadership. The supposed ultimate Republican objection to the bill is that it would make public funds available to finance campaigns. But the Democrats have reduced the public funding to a shadow role, while Mr. Dole is cheerfully accepting public funds to help finance his presidential campaign, and so far as we can see it hasn't hurt him a bit. Mr. Dole has the power to break the impasse on this legislation. He and the Senate would both be the better for it.

The problem with the present system is that it has no upper bound. The cost of office has raced ahead in recent election cycles until the parties are bidding for power with dollars. The average Senate winner spent more than $3 million in the last election. To amass that much a senator must raise $10,000 a week every week of his six-year term. A senator who expects a close race or is from a larger state may have to raise two, three or even four times that. They live with their hands outstretched. The House, where the average winner now spends more than $300,000, is not far behind. For senior House members particularly, a greater share of this money than is healthy comes from the PACs, the giving arms of interest groups.

The bill seeks to impose spending limits on Senate races only (the House would add what rules it chose for itself). The Supreme Court has said it is a violation of free speech to impose such limits absolutely; they would thus be voluntary, binding only on candidates who chose to accept federal funds. Even then not all candidates would get such funds -- only those who agreed to abide by the spending limits and whose opponents did not. In deference to the Republicans, the public funding has been reduced to an insurance policy. The bill would also limit the funds that either a House or Senate candidate could accept from PACs.

In the 1986 Senate elections, $182 million was spent. An expenditure that large corrupts the democracy in whose name it is made, and most senators know it. The bill that Sen. Byrd is championing would restore proportion. The Republicans should try to perfect and help to pass it.