Democrat Bill Bradley and Republican John McCain have mounted unexpectedly strong challenges to their party's front-runner presidential candidates as they emphasize an issue that most voters put far down on their list of importance: changing the campaign finance system.

These underdogs' call to reduce the role of money in politics will receive its greatest attention of the presidential campaign when the two meet in New Hampshire this morning for an unusual interparty appearance. Bradley and McCain will gather on the site of the much-ballyhooed 1995 handshake between President Clinton and then-House Speaker Newt Gingrich (R-Ga.) in which the two party leaders pledged to do something about the campaign finance system, and then promptly dropped the matter.

Bradley and McCain are coming together to promise something that they may have difficulty delivering even if they are the nominees: having their parties give up the large, unregulated "soft money" donations that have become a major element of presidential campaigning.

Their joint appearance raises the question of whether their pledge will be any more effective than the Clinton-Gingrich handshake that preceded them or, like the handshake, will have more political benefits than practical results.

The Bradley-McCain reprise--to be broadcast tonight on ABC's "Nightline"--offers both candidates a bonanza of free publicity, and a choice political opportunity to reinforce their twin images as reformers. In particular, it gives Bradley and McCain a high-profile chance to appeal to the independent voters who will be key to determining the winners from both parties in the Feb. 1 New Hampshire primary.

"The campaign finance issue has never had this kind of intensive treatment in a presidential campaign before," said Fred Wertheimer of Democracy 21, which has worked closely with McCain on his legislative proposal.

Still, only McCain has pledged to give up soft money unilaterally; Bradley's promise is contingent on having the Republican nominee get his party to turn down soft money as well.

Even if that were to happen and the nominees were to order the Democratic and Republican National Committees to reject soft money, moreover, the presidential candidates would have little control over the flow of such funds to congressional campaign committees and state parties, where it could be used to equal effect in voter turnout efforts important to the presidential race.

At the same time, today's event is likely to leave unstated the significant differences between the two candidates' approaches to changing the campaign finance laws.

Bradley supports public financing of congressional elections with a matching system similar to that used in the presidential race. McCain supports a limited taxpayer subsidy of congressional campaigns in the form of free television time and discounted rates for direct mail, but has stopped short of calling for public funding.

Both candidates are spending heavily on television advertising in Iowa and New Hampshire, but neither mentions campaign financing, a sign that today's meeting is as much about symbolism as it is about passion for a particular issue.

"They're both going to be able to attack their principal opponent without looking negative," said Tad Devine, a strategist for Vice President Gore. "If Bradley believed campaign finance was going to decide this election, he would not have health care ads on television."

For both Bradley and McCain, emphasizing reform has been a useful weapon against establishment front-runners. In a speech yesterday, for example, Bradley attacked Gore as "wedded to the ways of Washington" and said Gore "doesn't care about reform as much as preserving power."

"This is a way for Bradley to differentiate himself without moving any further left, and for McCain to differentiate himself without moving right," said Dennis Goldford, the political science chairman at Drake University in Iowa. "The average person says they hate to see the parties squabbling, and this plays right into that."

Colby College political scientist Tony Corrado said emphasizing campaign finance reform helps Bradley "highlight how little the Clinton administration has done and Gore's own campaign finance problems in 1996. In McCain's case, it sets up the contrast between him and the huge war chest [George W.] Bush has amassed."

Each has made campaign finance a part of his personal biography, complete with a moment of revelation that turned him off to the system. For Bradley, that was almost losing the 1990 Senate race despite raising $12 million. For McCain, it was his dealings with savings-and-loan kingpin Charles Keating and subsequent rebuke by the Senate Select Committee on Ethics.

But the discussion of campaign finance is a highly rhetorical debate in which even the candidates don't much mention the specifics of their proposals. For months, Gore and Bush stressed that they too supported reforms; just this week, Bush hit back at McCain for the first time on the matter, arguing in a debate Monday night that McCain's plan would hurt the Republican Party by causing it to give up soft money donations without imposing new restrictions on labor union giving.

"Bush scored a significant point there," said GOP pollster Linda DiVall. "There is a significant critique against McCain's proposal for Republican primary voters."

In South Carolina yesterday, McCain responded to Bush, arguing that "campaign finance reform is a conservative issue" and that conservative goals such as revamping the tax code will not be reached until the campaign finance system is changed.

However, pollsters in both parties note that campaign finance consistently ranks at the bottom of the list of issues the public wants addressed, and say that neither Bradley nor McCain appears to have registered specific gains in New Hampshire because of their campaign-funding proposals.

A September Washington Post-ABC News survey of the most pressing issues in the presidential race found that 30 percent of voters considered it "very important," the lowest of any issue polled.

And in New Hampshire, surveys in May and September by the University of New Hampshire's Survey Center of likely primary voters found only 2 percent who said campaign finance overhaul was their top priority.

Indeed, even backers of McCain and Bradley don't appear to put much extra emphasis on the issue. In the New Hampshire poll, for example, just 11 percent of McCain supporters said it was their top issue. Among Bradley supporters, the figure was just 2 percent who put campaign reform as their biggest priority, compared with 3 percent for Gore backers.

"It's just not a major issue any way you look at it," said Andy Smith, director of the UNH polling team.

In fact, voters don't even appear to connect the campaign finance crusade with McCain and Bradley. For example, a recent national survey by Harvard University for the "Vanishing Voter Project" found that only 10 percent of the 1,000 Americans polled could connect McCain with his signal campaign issue: banning unlimited soft money contributions to the political parties.

Indeed, more respondents--13 percent--actually thought McCain opposed a ban on soft money and a whopping 77 percent didn't know what his position on the issue is.

Even so, some political consultants and close watchers of this year's race suggest that Bradley and McCain have managed to tap into an issue that resonates with voters.

"It's true that campaign finance reform consistently registers about 2 percent," DiVall said, "but it's also true that when you conduct focus groups, you hear them talk about lobbyists, about special interest influence in Washington. That comment is much more pervasive than it was four or five years ago."

Still, many pollsters argue that the public tunes out when it comes to specifics. "All our polls indicate the public does think campaign finance needs major changes, but it's just not clear what should be done," said Dennis Moore, vice president of the Gallup Organization. "The proposals are so technical. Few people even understand what soft money is."

Staff writer Ed Walsh contributed to this report.

CAPTION: GOP's John McCain, campaigning at Converse College in Spartanburg, S.C., is not in total agreement with Democrat Bill Bradley on campaign financing.