WASHINGTON -(Dow Jones)- Congressional Democrats appear increasingly poised to move forward on health-care legislation, despite last-minute squabbles over how the bill handles abortion coverage.

Senate Majority Leader Harry Reid (D., Nev.), in a letter Thursday to Senate Minority Leader Mitch McConnell (R., Ky.), issued in absolute terms what Democrats have for weeks implied: They plan to move forward on the bill using a fast-track legislative tactic known as budget reconciliation. The method allows them to pass the bill with the support of 51 senators, rather than the ordinary threshold of 60.

"We will finish the job," Reid said in the letter. "We will do so by revising individual elements of the bills both houses of Congress passed last year, and we plan to use the regular budget reconciliation process that the Republican caucus has used many times."

House Democrats met for hours Thursday, as White House Office of Health Reform director Nancy-Ann DeParle briefed them on the contents of the measure that Democrats want to pass under reconciliation. That bill--the second part of a two-bill strategy--would make changes to a broader health-care bill already passed in the Senate and awaiting a vote in the House.

It is expected that under the changes, the overall legislation would cover more of seniors' drug costs under the Medicare Part D. Also, a tax on high-cost insurance plans would be delayed until 2018, and states would receive more aid to help pay for an expansion of the low-income Medicaid program.

The legislative language changing the Senate bill has been sent to the nonpartisan Congressional Budget Office. Democrats say they are awaiting a final cost estimate from the CBO before they move forward.

"Our clock starts ticking when we get the CBO report," said House Speaker Nancy Pelosi (D., Calif.). She added that caucus members will have "at least one week" from that time before they will be asked to vote on anything.

"It is not something that we are going to drag out, because the decisions are made," Pelosi said.

Abortion remains a key sticking point. Rep. Bart Stupak (D., Mich.), an anti-abortion Democrat, has suggested that he has the support of as many as 12 Democrats to stiffen the abortion language currently in the Senate bill. Abortion-rights Democrats--who already think that the Senate bill goes too far to prevent the federal funding of abortion--say they will not allow Stupak to change the language.

"Ironically, we have a situation with abortion that neither side is very happy about," said House Energy and Commerce Chairman Henry Waxman (D., Calif.)

Some lawmakers have speculated that a commitment could be made to Stupak to change the abortion language after the health-care bills pass, perhaps through an appropriations bill. But Rep. Dan Lipinski (D., Ill.), an abortion opponent, suggested that Stupak's group is seeking tweaks to the abortion language in the bill that will change the original Senate bill.

"There is no promise or guarantee I'm looking for," Lipinski said. "I'm looking for a change in the reconciliation bill."

Likewise, Rep. Jan Schakowsky (D., Ill.), a member of the Congressional Pro-Choice Caucus, said that abortion-rights lawmakers are "not going to support any kind of side deal."

She also suggested that Stupak doesn't actually have the commitment of 12 members to vote against the legislation unless it is changed, saying that many anti-abortion Democrats "understand that there is no federal funding for abortion in the bill."

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