Washington (CNN) -- Senate debate on a sweeping health care bill proceeds to one of the most controversial issues Monday: an amendment to tighten restrictions on federal funding for abortion.
The amendment by moderate Democratic Sen. Ben Nelson of Nebraska would mirror language from the health care bill passed by the House last month that prevents any health plan receiving federal subsidies from offering coverage for abortion. It was unclear if a Senate vote on Nelson's amendment would occur Monday.
Anti-abortion legislators say the House language that Nelson seeks to adopt maintains the current level of restriction by preventing any federal funding for abortion, except in the case of rape, incest or a threat to the life of the mother.
Opponents of the tougher language say the amended language would expand the current level of restriction because women receiving coverage under a federally subsidized health care plan would be barred from purchasing abortion coverage with their own money.
"You can't use private money in the private market ... and frankly, I think that goes too far," Sen. Claire McCaskill, D-Missouri, said Monday on the CBS program "The Early Show."
The House adopted the restrictive language as part of a last-minute concession to anti-abortion legislators who threatened to defeat the health care bill without a vote on the provision.
A similar dynamic could exist in the Senate, with anti-abortion Democrats preventing final approval of the health care bill if they don't like the abortion language.
The activity comes a day after President Obama met with Democratic senators amid a rare Sunday session for the Senate as it considers the Democratic proposal that so far is unanimously opposed by Republicans.
White House spokesman Bill Burton said Obama "thanked members of the Senate for their hard work so far and encouraged them to continue forward on this historic opportunity" to pass health care reform legislation.
"The question now is whether or not we're going to get it done," Obama told the senators, according to Burton.
Meanwhile, a group of moderate and liberal Democrats met again Sunday afternoon to try to work out differences over tough issues such as a government-run public health insurance option.
The group, put together by Senate Majority Leader Harry Reid, a Nevada Democrat, has been meeting regularly to seek Democratic consensus on the public option and other issues threatening the ability of Democrats to overcome a Republican filibuster.
"There are still a few things to work out in the bill," Reid said, adding that "the issues were being narrowed," but "we're not there."
On the Republican side, Senate Minority Leader Mitch McConnell of Kentucky on Sunday repeated past criticism that the health care bill ignores GOP concerns and issues.
"There was no interest in drafting a proposal that was in the political middle," McConnell said, adding that Democrats wrote a bill "that Republicans couldn't in good conscience support."
Reid denied the claim, saying Republicans had plenty of opportunity for input in the months of debate and scores of committee hearings so far. The lone goal of Republicans is to defeat the bill to cause political harm to Obama and the Democrats, Reid said.
"Republicans are being destructive," Reid said. "They want this to be, as one senator said, President Obama's 'Waterloo,' and it's not going to be."
The public option is among the most contentious issue for Democrats, with two members of the caucus saying they have yet to see a compromise they can support.
The Democratic caucus contains 60 seats in the 100-member chamber, which is the minimum number needed to overcome a filibuster. If any Democratic caucus members balk at the public option, the party would need some Republicans to back the bill in order for it to pass.
The House has narrowly passed a more than $1 trillion health care plan.
If the Senate also manages to pass a bill, a congressional conference committee would then need to merge the House and Senate proposals into a consensus version requiring final approval from each chamber before moving to Obama's desk to be signed into law.