Democratic leaders in the House would be happy to concede to the Senate version -- liberal members of the party were unhappy with the abortion language inserted in the bill -- but Stupak told ABC News last week he will not vote for a bill that does not include his language. There are several anti-abortion Democrats in the House who insist on this as a condition to pass the bill.
"Our members are holding, so we will not pass if they are putting anything but a version of our language," Stupak said.
The Senate plan does not include the option of a government-run insurance plan, a thorny issue among Democrats. The plan initially had a public option in which states would have the choice of whether they wanted to participate. But Democratic leaders did away with that provision to appease lawmakers such as Nelson and independent Sen. Joe Lieberman of Connecticut.
The House health care bill, however, includes a public option in what becomes one of the biggest health care policy differences between the two bills. Under the House's public option plan, the government would negotiate rates with insurance companies instead of setting fees, as it does in Medicare.
At least 50 Democrats in the House are on the record as saying they will not vote for a bill without this option while Nelson and Lieberman have refused to support a bill that does include a public option.
President Obama Monday tried to downplay the differences over the public option, saying that debate is not the most important aspect of the bill.
"This is an area that has just become symbolic of a lot of ideological fights. As a practical matter, this is not the most important aspect to this bill -- the House bill or the Senate bill," the president said in an interview with American Urban Radio Networks, adding that "the Senate and the House bills are 95 percent identical."
Obama, who had initially pushed for a public option, spoke of the plan in the past tense.
"It was only going to apply to a few million people who were buying into the exchange," Obama said. "So it wasn't like suddenly everybody would just go out there and buy a government-run plan; most people will still get health insurance from their employers. What will happen is, is that if you don't get health insurance through your employers, you can then go to this what we're calling a health care exchange, get a subsidy and buy health insurance through that exchange."
ABC News' Jonathan Karl and Dr. Tim Johnson contributed to this report.