At last week's conference, Morgannwg LMC proposed that GPC Wales should negotiate with the Assembly government to take back control of out-of-hours care and the associated funding.
Swansea GP Dr Charlotte Jones told the conference: 'Many GPs are fed up with being portrayed by the media as uncaring.
'We handed the government an own goal by giving up our out-of-hours responsibilities.'
She added that GPs could commission other providers, rather than offering the service themselves.
But the motion was met with hostility from GPs from more rural parts of Wales, who warned it could add to the country's recruitment problems. One said the proposal 'would go down like a cup of cold vomit'.
Dr David Bailey, GPC Wales chairman, said: 'We'd be condemning a number of our colleagues in rural areas to getting up in the middle of the night to visit patients.'
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