WASHINGTON (AP) _ Frustrated sponsors of campaign finance legislation said Wednesday they will bring their bill to Senate debate in September, one way or another, and President Clinton supported their move.

``The time to act on this matter is rapidly expiring,'' said Sen. John McCain, R-Ariz., co-sponsor of the most prominent of some 70 campaign finance bills floating around the Capitol.

He said he would try to persuade Majority Leader Trent Lott, R-Miss., to bring up his bill as a free-standing measure. But if that fails, McCain said he would offer it as an amendment to an unrelated measure.

Clinton said Wednesday the campaign finance system ``has been overwhelmed by a flood of campaign cash'' and has pitted the two political parties in an ``ever-escalating arms race'' for more.

``To make sure that ordinary citizens have the loudest voice in our democracy, we must act to change the campaign finance laws,'' he said in a statement. ``September will be the time for members of the Senate to stand up and be counted for reform. I will do what I can to see to it that 1997 is finally the year that it is achieved.''

The bill sponsored by McCain and Sen. Russell Feingold, D-Wis., and backed by Clinton would ban the unlimited ``soft money'' contributions to parties that have grabbed headlines and would authorize voluntary spending limits for candidates in exchange for reduced broadcast advertising costs.

Both McCain and Feingold said they welcome suggestions on ways to improve it but they will stick to the soft money ban and efforts to level the playing field between incumbents and challengers.

``We now live in a country where any millionaire can dream of growing up to be a senator,'' said freshman Sen. Susan Collins, R-Maine, one of the bill's 33 co-sponsors.

In an interview, Feingold said he and McCain picked September for Senate action because it must be done in time to establish rules for next year's campaigns. The budget prevented earlier action, and the 1998 campaigns, with lawmakers out seeking re-election, will prevent action then, he said.

``We want to give our colleagues and especially the American people plenty of notice that this is coming up,'' Feingold said. ``We need public pressure to pass this, and you won't get public pressure unless they know something's coming up.''

Collins said lawmakers ``should be embarrassed by how our system is viewed,'' she said, referring to comments by Johnny Chung, a major Democratic contributor. The Los Angeles Times quoted him Sunday as saying: ``I see the White House is like a subway _ you have to put in coins to open the gates.''

``The vast majority of honest and hard-working Americans do not have enough coins to open the gate,'' Collins said.

In the House, Rep. Christopher Shays, R-Conn., co-sponsor of a similar bipartisan bill, has threatened to force a vote this year by getting fellow Republicans to buck party leaders and vote with Democrats to bring it to the House floor. It would only take 11 Republicans if Democrats all support it.