Senate Finance Committee Chairman Max Baucus, D-Mont., told single-payer advocates Wednesday that he regrets not allowing more discussion of the single-payer plan in his efforts to draft a health system overhaul proposal, according to participants at the meeting.

Five advocates of the single-payer system – now largely dismissed by most as politically unfeasible – held a press conference Wednesday afternoon with Sen. Bernie Sanders, I-Vt., to discuss the private meeting with Baucus. During the meeting, the advocates pledged to continue pushing single-payer as a mechanism for reform.

As the Finance Committee and the Senate Health, Education Labor and Pensions Committee ready their reform bills, many Democrats are throwing their support behind a public plan that allows the government to compete with private insurers in an insurance marketplace. A single-payer system would have the government cover the costs of care.

Sanders called the meeting with Baucus “useful and productive” but said he knew that Baucus wouldn’t change his mind about not backing a single-payer system.

“But I think it’s fair to say when he said something to the effect that ‘single payer is off the table,’ I think he regrets having said that,” Sanders said.

Sanders strongly supports a single-payer approach, and said it is” incomprehensible” to pursue a health care overhaul without “engaging in serious discussion about a single-payer health care system.” Such a system ideally would be administered by states, he added.

Dr. David Himmelstein, co-founder of Physicians for a National Health Program and associate professor of medicine at Harvard Medical School, said Baucus did tell the group he would try to have criminal charges dropped in the case involving single-payer protestors who recently disrupted a Senate Finance Committee meeting.

Geri Jenkins, co-president of the California Nurses Association, said Baucus told the advocates he feels the process is too far along to seriously consider inclusion of a single-payer plan and that he didn’t think it would pass. The advocates said they were undeterred. “We will continue to push forward with it in every venue we can,” said Jenkins, a registered nurse.

Baucus’ spokeswoman didn’t immediately return a phone call seeking comment.