Derbyshire CC Unison members are being asked to vote on a one-day strike for 5 April, while Unison members in Birmingham are considering a day of action for 4 April.
Derbyshire is considering its action to protest against planned cuts of over £30 million which Unison says will put more than 1,000 jobs at risk. Birmingham has said it will have to lose 600 jobs to accommodate cuts of £41m.
Both branches made it clear the action was directed against the government, rather than the local authorities themselves.
Other Unison branches which organised lobbies and rallies, though not industrial action, include Sunderland, Sheffield, Lothian and Highland.