The sweet success of a Valentine's Day victory was savored with a celebration for backers of the most sweeping campaign finance reform since the 1970s.

House passage of the Shays-Meehan legislation, named after its sponsors, came in the wee hours of the morning Thursday and backers cast its passage in historic terms.

But now the measure goes to the Senate where a new battle is already underway. Senate Majority Leader Tom Daschle, D-S.D., tried unsuccessfully to keep the momentum going by bringing the measure up as soon as possible on the Senate floor Thursday, but was promptly stopped by Kentucky Republican Sen. Mitch McConnell, the chamber's most strident opponent of campaign finance reform.

McConnell accused Daschle of breaking his promise to bring energy policy to the Senate as the next big issue — something Republicans have wanted to deal with for months.

Campaign finance reform opponents also want to read the fine print in the House-passed version of the bill.

The two political parties and their various campaign committees raised more than $500 million combined in soft money in the two years that ended in 2000, and have continued to raise money in large amounts in the months since.

While banning soft money to the national committees, the legislation would permit such donations to state and local parties, so long as the funds were not used in connection with federal campaigns.

Supporters say the legislation would help curtail late campaign "issue ads" that have proliferated in recent years, by prohibiting the use of soft money to pay for them to be broadcast within 60 days of an election or 30 days of a primary. These ads are typically purchased by interest groups, and while they stop short of expressly advocating the victory or defeat of a candidate, they are often harshly critical.

The measure also would allow candidates to raise direct hard money contributions from individuals to $2,000 per election, an increase from $1,000.

Another provision, added during debate, stripped out a requirement that would have tightened an existing law requiring political broadcasting to be sold at a preferential rate. The legislation's backers nominally opposed the amendment — but the National Association of Broadcasters supported it — and Reps. Christopher Shays, R-Conn., and Marty Meehan, D-Mass., carefully avoided calling it a "poison pill" that would doom the measure.

McConnell may launch a filibuster, which would require supporters to get 60 votes to pass it, in order to kill the bill. But Sen. Ernest Hollings, D-S.C., said he could be the 60th vote. Having opposed the bill the first time it came to the Senate floor, Hollings said he would support it this time.

Sen. John McCain, R-Ariz., a principal sponsor of the Senate bill, told McConnell it's time to throw in the towel.

"I'm optimistic about getting the 60 votes if necessary. I hope it's not necessary ... I hope McConnell would appreciate that it's time to fold the tent," McCain said.

McCain said the White House has already indicated that the president would sign the bill if it passed both chambers of Congress.

Overall, the White House remained noncommittal. White House spokesman Ari Fleischer said, "The president will wait to be declarative until he sees what the final bill is."

Fleischer did indicate the president's desire to sign a measure into law that improves the system and this bill has a good chance of becoming law.

"He wants to sign a bill that improves the current system. Parts of that legislation surely do. Other parts are not fully consistent with the president's principles."

McConnell did seem resigned to passage of the bill in the Senate, telling reporters he would be the lead plaintiff in a lawsuit to be filed if the bill became law.

John Feehery, a spokesman for Speaker of the House Dennis Hastert, R-Ill., said the formal paperwork would probably be sent to the Senate in a few days, while Congress is at recess for the President's Day holiday.

Fox News' Carl Cameron and The Associated Press contributed to this report.

Carl Cameron currently serves as Fox News Channel's (FNC) Washington-based chief political correspondent. He joined FNC in 1996 as a correspondent.