WASHINGTON (Reuters)—Democratic leaders in the U.S. Senate said on Tuesday they hope to bring a long-delayed health care reform bill to the floor next week, kicking off a tough fight that may well spill into next year.

A vast health care overhaul has been stalled in the Senate for a month but gained new urgency on Saturday when the House of Representatives passed a bill designed to rein in costs, extend coverage to millions of uninsured and bar practices such as denying coverage to those with pre-existing conditions.

Democratic Senate leader Harry Reid of Nevada and his No. 2, Dick Durbin, D-Ill., said they hoped to bring the Senate's health care bill to the floor next week and to have the first procedural vote on whether to open debate.

But Sen. Durbin said it would be difficult to meet President Obama's goal of signing a bill on reforming the $2.5 trillion U.S. health care system by the end of the year.

"I hope so, but just count the days," Sen. Durbin told reporters when asked if they could meet President Obama's deadline. “Our goal is to make sure it is out of the Senate this year," Sen. Durbin said.

That would mean negotiations to reconcile the House and Senate versions would occur in January, and each chamber would have to pass the merged bill again before Obama could sign it into law.

"I wish we could complete it this year. But if we don't, we will get it done," Sen. Durbin said.

Former President Bill Clinton, who failed in a 1994 effort to revamp the health care system, spoke to Democratic senators at their weekly lunch in an effort to jump-start the effort in the Senate.

Sen. Reid has been waiting for weeks for cost estimates on the Senate's version of the bill and searching for an approach that can win the 60 votes needed to overcome Republican procedural hurdles.

President Obama and Democratic advocates have pushed for quick passage to prevent the health care issue from becoming entangled in the 2010 congressional elections, when all House members and one-third of the 100 senators face re-election.

Republican opponents hope dragging out the process will allow more time for public opposition to mount, as it did in August when lawmakers went home for a one-month recess and faced sometimes fierce criticism from voters.

Sen. Durbin said President Obama is pushing for action.

"The president called me yesterday, and I know what he wants and I share it—to bring this health care reform bill to him as quickly as possible," Sen. Durbin said.

"I also believe that (President Obama) will play a critical role in the passage of this bill," Sen. Durbin said. "So we are counting on him, and we are going to be working with him very closely."

The Senate action has been complicated by the House's adoption of a provision tightening restrictions on the use of federal funds for abortion, a move that has angered Democrats who support abortion rights.

Sen. Reid voiced confidence the Senate would be able to find a compromise to avoid a confrontation on the abortion issue.

"I do believe we can work that out," he told reporters. "We need to work this out and we will."