The poll was sent via email to about 10,000 physician leaders who are members of the American College of Physician Executives, after the first presidential debate between Romney, the Republican nominee for president, and President Barack Obama, the Democratic nominee.
The survey drew 422 responses and of those, 47.2 percent said they believed Romney's plan would be more effective in shoring up Medicare financial processes and serving the Medicare population.
Thirty-three percent said they supported President Barack Obama's plan. An additional 10.2 percent didn't support either plan and 8.2 percent didn't watch the debate.
Obama favors keeping Medicare as a government-run program while reforming the current payment system and reducing fraud. Romney embraced running mate Paul Ryan's plan to overhaul the entitlement program and convert it to a voucher system that would require seniors to buy private health insurance with government subsidies.
Participants in the poll were allowed to post comments anonymously. One participant appeared summed up the feelings of many by praising Romney and Ryan for being willing to discuss a new approach to Medicare.
"The road to long-term national fiscal stability will require major changes in both the healthcare delivery and reimbursement systems, and must entail serious reform of Medicare ... Romney and Ryan are honest enough to discuss this issue, and will be flexible enough to find a workable solution."
But many disagreed and expressed skepticism at the idea of privatizing Medicare.
"At least we know Obama's plan and it is partially executed. We need time to see this out and then make adjustments as needed, not start all over to reform healthcare," another respondent wrote.