A spokeswoman for Cornwall Council said it had received no formal notification of Collin Brewer's intention to resign, despite reports that the independent councillor has quit his job.
Cllr Brewer faced calls to go yesterday after it emerged he had suggested that disabled children "should be put down" to save money.
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David Cameron said the measure, which will save £4 million by 2020, showed a commitment to his "all in this together" approach.
The party has dropped its opposition to an in/out referendum on EU membership and now supports a vote, acting leader Harriet Harman said.