A group in the city's Queen Street shopping area gathered on Sunday to attack the "introduction of the private sector into public service provision."
The party paraded new Plaid sympathisers who were formerly members of the Labour party.
Member Wayne Beard said: "I find the prospect terrifying and a betrayal of the values of the party I joined as a young man.
"New Labour may not have an ideological objection to putting shareholders before schools; profit before patients. Plaid Cymru emphatically does and so, I believe, do the people of Wales."
Mr Beard accused the Government of "political cowardice on a grand scale" in moves to supplant the NHS with private funds.
Llanelli GP Dr Chris Slader, another defector, said: "Introducing a profit motive into health provision is not the answer.
"Private companies exist to make money. That will always come first for them."
Health matters are devolved to the Welsh Assembly, but Westminster retains power over medical regulation and safety.
The last Conservative administration was criticised for a "creeping privatisation" of the health service, and the party has pledged to increase private health care options if it wins the next General Election.
Labour has indicated a similar plan, but the party insists care would be carried out within the NHS and not outside the system.
In November 2000, Health Secretary Alan Milburn signed a deal which allows NHS patients to be treated in a private hospital.
The Private Finance Initiative - introduced by the Conservatives in 1992 and now supported by Labour - allows hospitals to access extra funds.