Sen. Casey's compromise included an increase in a tax credit for people who adopt a child, funding to help pregnant teens and others with alternatives to abortion and stronger language to protect health care providers who don't want to perform abortions. But it is unclear whether it went as far as the Stupak-Pitts amendment in the House bill, which would not only cut federal funding for abortion-related services, but would also limit access to abortions for people who receive federal subsidies and those who purchase insurance through a health insurance exchange, a marketplace where people would be able to shop for and compare insurance plans.
Rep. Bart Stupak, D-Mich., rejected the Casey proposal as a "non-starter," and expressed confidence that his language will be included in the final bill. Stupak told ABC News he has been in touch with Sen. Nelson.
"They are holding tough and they are asking me, 'Is the House holding tough?'" Stupak said, referring to his Senate counterparts like Nelson and Sen. Orrin Hatch, R-Utah, who crafted the abortion amendment in the Senate health care bill. "Our members are holding, so we will not pass if they are putting anything but a version of our language."
Nelson, a former insurance industry executive, has been something of a star in Nebraska's Democratic party. Hailing from a relatively conservative state, he has enjoyed a long public service career and is currently the only Democratic candidate from the state in Congress.
But while he enjoys local success, he has butted heads with fellow Democrats in Nebraska several times, especially on the issue of abortion.
As governor, Nelson signed a ban on so-called partial-birth abortion that was overturned by Nebraska's Supreme Court in 2000.
He also backed the nomination of Supreme Court nominee Samuel A. Alito Jr. despite Democrats' objections to the judge's anti-abortion position.
Nelson, who was born in Nebraska and has lived all his life there, is also a member of anti-abortion organizations and, during his campaign, was endorsed by several of them.
Nelson sees a tough battle in 2012, when his term expires. The Nebraska senate race is expected to be a competitive one as Republicans step up efforts to reclaim Nelson's seat, which has been occupied by a Democrat for more than two decades.
It is no surprise then that Nelson has been so steadfastly fixed on the idea of introducing firmer language on abortion in the Senate health care bill.
"Federal taxpayer money ought not to be used to fund abortions," Nelson told ABC News' Jonathan Karl in November. "So whether it is subsidies on premiums or whether it is tax credits or whatever it is... it should not be used to fund abortions."
Bob Kerrey, who held the senate seat before Nelson and is now president of the New School in New York, said the anti-abortion group is a formidable force in Nebraska politics, and their pressure on lawmakers is enormous.
"It certainly accounted for a significant part of my opposition because I held the opposite view," Kerry told ABC News. However, Kerrey differs with Nelson on the issue, arguing that one should make a "decision on what you believe the law should be, not what you believe about the action."
Nebraskan Democrats have raised little ruckus over the deadlock on the abortion issue.