WASHINGTON — Advocates of an overhaul of the nation’s scandal-scarred campaign finance system renewed their crusade in the Senate on Monday, but conceded they lack the muscle to overcome a Republican-led filibuster.

“As far as I can tell that’s just not there yet,” said Sen. Joseph Lieberman, a Connecticut Democrat who served on the panel that investigated questionable practices in the 1996 presidential campaign. “Right now, we don’t have the 60 votes.”

Senate Majority Leader Trent Lott made clear he won’t permit the bill to linger long on the floor. “We have a lot of things to do and we don’t have a lot of time,” the Mississippi Republican told reporters shortly before debate began. “I don’t see it going beyond the end of the week.”

The measure, drafted by GOP Sen. John McCain of Arizona and Democratic Sen. Russ Feingold of Wisconsin, would ban unregulated “soft money” to national political parties from corporations, labor unions and individuals. It also would provide fresh curbs on advertisements that attack candidates but escape regulation because they are presented as “issue ads” not covered by existing election law.

There has to be a “different vision” than the current system, said Feingold, something other than coffee with President Clinton in the White House for wealthy donors or well-heeled special interests traveling to Florida to share lunch with Lott, who leads Senate Republicans.

Most Republicans, led by Lott, have countered with a proposal that would require organized labor to obtain the consent of members before using their union dues on political advocacy.

“Support for paycheck protection is the litmus test of whether we are serious and whether we are credible” about revising campaign laws, Lott said on the Senate floor. “Workers of America are mugged every time they are forced to contribute to candidates and to causes they do not support.”

The first vote is scheduled for today on a GOP attempt to table, or kill, the McCain-Feingold proposal.

That is expected to fail, but leave the legislation’s supporters well short of the 60 votes they would need to choke off a filibuster and force Lott and other opponents to the bargaining table.

The battle is expected to turn eventually to a compromise by Sen. Olympia Snowe. Rather than Lott’s call to give individual union members more say over the use of their dues, she and other GOP moderates have countered with a proposal to require speedy disclosure of contributors to any broadcast commercials targeting specific candidates within 30 days of a primary or 60 days of a general election.

In addition, it would prohibit the use of union or corporate funds for such ads. It would “simply require funding to come from sources traditionally relied upon for campaign purposes — PACs [political action committees] or individual, voluntary donors,” according to a summary of the legislation.

Several congressional sources, speaking on condition of anonymity, said Snowe is offering to join Democrats in voting to kill Lott’s union proposal if all 45 Democrats will swing behind her alternative. While Feingold and a few other Democrats are urging that course as a step forward toward passage of their proposal, Democratic Leader Tom Daschle of South Dakota has not said what he intends to do.