President Obama's proposal, released last week, builds on the Senate health care bill, which includes less-restrictive language on abortion than the House bill. But those who support the language in the Senate bill and the president's proposal say it maintains the existing law.
"I hope that when the bill is in its final form and people have a chance to look at it, I think they will understand that this bill does not change the status quo on abortion," Sebelius said.
The language in the Senate health care bill restricts the use of public funds for abortion services. But private insurance plans that are offered in the insurance exchange can cover abortion if funds for the procedure are used only from premiums paid by beneficiaries. States have the option of banning coverage in insurance plans brought in insurance marketplaces.
Stupak's amendment, which was part of the House bill but failed in the Senate, limits 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.
Stupak's more restrictive anti-abortion language passed the House by a vote of 240-194. Senators defeated the anti-abortion amendment 54-45, and that Obama is pushing.
Stupak said the abortion language can be included even through reconciliation, a process which does not require 60 votes but a simple majority of 51 senators to pass.
"You can do it, if there's a will there's a way," he said. "That's just the excuse they're giving."
The issue of abortion has sparked nationwide debate. Anti-abortion groups vigorously oppose the legislation being discussed but groups that favor abortion rights say the House's language would move the federal government into a whole new area of restricting women in the private insurance sector.
Stupak said he talked to the president in September and expressed his concerns about the abortion language. He said he has repeatedly told the Democratic leadership in the House that they have to include the language to garner full support, but has been told that it's hard for the leadership to do that.
The congressman from Michigan does not think there are enough votes in the House to pass the health care bill as it currently stands, and called the Senate bill "totally unacceptable."
"I'm not involved in the head count but they are lucky if they have 150 votes," Stupak told ABCNews.com. "They have to make a lot of improvements in order to get House members to vote for it. Members are not enamored with the process or contents of the bill."
The president on Wednesday launched his final push to get health care legislation passed, indicating a willingness to work with Republicans on some issues but telling Democrats to use Capitol Hill's controversial reconciliation rules to get a bill to his desk if necessary.
"The president is talking about Congress moving again on bills that have already passed," Sebelius said today. "And I think the American public deserve an up or down vote."
"It's urgent... and we need to figure out how to move forward as quickly as possible," she added.
Republicans have been grousing for weeks about the use of reconciliation, saying it shortcuts the process and should not be used for a bill of such importance.