House Majority Whip James Clyburn (D-S.C.) predicted Sunday that a key Democratic critic will ultimately support a health care reform bill that is headed to a vote as early as this week.

“I do believe that Congressman [Bart] Stupak will end up voting for this bill,” Clyburn said of the Michigan Democrat on NBC’s “Meet the Press.”

Along with other House Democratic leaders, Clyburn worked furiously in recent weeks to assuage the concerns of Stupak, an abortion-rights foe who successfully led the charge last year to strike federal abortion-related funding provisions from the House’s health care package.

With threats of a GOP filibuster forcing House Democrats to take up the already-passed Senate bill, which includes less stringent abortion language, the votes of 41 House Democrats who do not support abortion rights continue to hang in the balance. But on Sunday, Clyburn said the recent endorsement by the Catholic Health Association is an indication that the concerns of Stupak and other fence-sitting Democrats have been met.

“We just had the Catholic hospitals endorse this bill,” Clyburn said. “I don’t think they’d be doing that if they were not comfortable with this language.”

But the House Democrats’ chief vote counter said he is still corralling support for the bill, although he is “very confident that we’ll get this done.”

“We don’t have [the votes] as of this morning, but we’ve been working this thing all weekend. We’ll be working it going into the week,” Clyburn said. “I have been talking with Members for a long time on this, and they have the will do it. They’ve been looking to us to create a way to do it. We’ve gotten to a place where we do have a way to do it, and I think Members are going to vote for this.”

Clyburn agreed with Senate Majority Whip Dick Durbin (D-Ill.) that there is growing support in his Caucus for allowing the Senate to pass fixes to the legislation ex post facto.

“There is this historic distrust that exists between the two bodies, but I believe sincerely that we have been working together. … I think we’ve gotten a comfort level with each other,” Clyburn said.

Durbin said Senate Democratic leaders are currently shoring up commitments from Members that they will follow through on promises to enact House-backed health care provisions under budgetary rules that require only a simple majority for passage.

“When I served in the House, we used to say in the House Democratic Caucus, ‘The Republicans are our opponents, but the Senate is the enemy,’ so I can understand the building skepticism and the lack of trust,” Durbin said on “Meet the Press.”

Durbin added, “When [Speaker] Nancy Pelosi goes before her House Democratic Caucus, it will be with the solid assurance that when reconciliation comes over to the Senate side, we’re going to pass it.”