On July 21, the Savannah Democrat voted against the bill - supported by President Obama - in the House Energy and Commerce Committee.
But Jeanne Seaver, co-founder of National Right of Communities Association, says Barrow might backslide when the full House votes.
He is one of several dozen fiscally conservative Blue Dog Democrats in the House who have been leery of the measure.
Like him, the association has voiced concerns about the scope and costs of the trillion-dollar-plus plan. The group also opposes a provision calling for optional "end of life" counseling for the terminally ill.
And it wants the legislation to address medical practice lawsuits, which it says drive up health care costs.
"A health care reform bill without tort reform is like a truck without tires." Seaver said. "It's simply not going to function well."
Last week, Barrow met in his Savannah office with Seaver and Sandra Holland, the association's other cofounder.
"The meeting didn't go very well," Seaver said. " ... John said that he will vote for a bill that is 'good enough.' "
"I don't think 'good enough' should be the standard by which you fundamentally change the best health care system in the world."
Seaver and Holland also lamented that Barrow won't hold another town hall meeting in Savannah.
Moreover, they complained that he rejected their petition because some people who signed it don't live in his 12th Congressional District.
"Am I missing something?" Holland asked. "Savannah contains about a quarter of the 12th District's population. How can a representative represent if he won't listen to the people he's supposed to be representing?"
Actually, Barrow aide Jane Brodsky said, she and Seaver are missing several things.
"First of all," Brodsky said, "the bill the House votes on is likely to be a lot different than what that the committee voted on."
Yet to be considered, she said, are versions passed by other House panels and changes likely to be made on the House floor. And the House might have to act on additional changes that could be made later by the Senate, she said.
"The congressman will have to consider what the bill looks like when it comes up for a vote," Brodsky said. "It's a long process."
Concerning what Barrow thinks is "good enough," she cited his recent opinion piece in the Savannah Morning News.
Barrow wrote that the bill fails to control costs and places new burdens on small businesses and people who already pay for their own insurance.
"In the end," he wrote, "reform we can't afford to pay for is reform that can't realistically happen."
He also said the committee voted on the bill without considering scores of pending amendments. Everyone would have benefited from "another month to read the entire bill, understand its ramifications, and make the bill better," he said.
Brodsky said Barrow had a town hall meeting in Savannah as recently as July 1. While it focused on veterans affairs, health care reform also was discussed, she said.
She said he has a series of town hall meetings scheduled for other parts of the district.
"You have to remember that there are 22 counties in the district," Brodsky said.
She said he respects petition signers who live outside the 12th but thinks they should take their concerns to their own congressmen.
Some groups have lobbied Savannah's other congressman, Republican Jack Kingston, on the bill. But because he is a staunch foe of the measure, they have spent less time on Kingston.
In contrast, Barrow has been a magnet for advocates on both sides because he has been perceived as persuadable