WASHINGTON – Newly elected party leaders in the Senate promised Tuesday that the new 50-50 era will be one of cooperation, but they already appeared to be heading for a fight over the issue of power-sharing.

“We are absolutely committed to reaching out and working together,” Senate Majority Leader Trent Lott, R-Miss., said as he introduced his new leadership team. “Different times call for different approaches.”

The Senate will be evenly divided at 50-50 if George W. Bush wins the presidency and Democratic vice presidential nominee Joseph Lieberman stays in the Senate. That scenario still gives Republicans nominal control because Dick Cheney would become not only vice president of the country but also president of the Senate with a tie-breaking vote.

Nevertheless, Democrats, who picked up four Senate seats in the election, are demanding parity in committee assignments and funding and setting the legislative agenda. “We will not be satisfied with anything less than 50-50,” said Senate Minority Leader Tom Daschle, D-S.D.

He said the options to be considered when he takes up the issue with Lott in the coming days will include committee co-chairs, rotating committee chairs or giving Democrats some chairmanships.

Republicans quickly downplayed those possibilities. “Republicans will be in the majority,” Lott said. “Somebody has to be in charge, and we will be very clear about what we do there.”

“It’s very hard to drive a car if two people are controlling the wheel at the same time,” said Sen. Don Nickles of Oklahoma, who retained his post of majority whip, the second-highest ranking Senate Republican.

Conservatives continued to dominate the GOP leadership, with the return of Lott and Nickles, elected without opposition, and Larry Craig of Idaho as Policy Committee chairman. Craig edged out Sen. Pete Domenici of New Mexico, 26-24. Another conservative, Sen. Rick Santorum of Pennsylvania, defeated Christopher “Kit” Bond of Missouri 30-20 to become the new Republican Conference chairman, with Kay Bailey Hutchison of Texas taking the conference vice chairwoman position and Bill Frist of Tennessee named to head the Republican Senatorial Campaign Committee.

Hutchison is the first woman to enter the Senate GOP leadership since Maine Sen. Margaret Chase Smith in the 1960s and 1970s, Lott said.

The top two Democratic leaders, Daschle and Democratic Whip Harry Reid of Nevada, were re-elected without opposition.

Other officers are Barbara Mikulski of Maryland, secretary of the caucus; John Breaux of Louisiana, chief deputy whip; Byron Dorgan of North Dakota, chairman of the Democratic Policy Committee; John Kerry of Massachusetts, chairman of the steering and coordination committee; Jay Rockefeller of West Virginia, chairman of the technology and communications committee and Patty Murray of Washington, the new chairwoman of the Democratic Senatorial Campaign Committee.

Lott and Daschle both said they hope to work out committee assignments and other power-sharing issues before the new Congress convenes Jan. 3. Without an agreement, both parties could filibuster the resolution on new committee slates, paralyzing the start of the session.

For 17 days after the Senate convenes, until the new president is sworn in Jan. 20, Vice President Al Gore will still be president of the Senate, giving Democrats the tie-breaking vote.

“For 17 days we will rule the world,” said Mikulski. “The other 300 days we will lay the groundwork for truly ruling the world.”

Daschle said Democrats will not try to take advantage of that brief time in power.