Cllrs Gwenfair Jones, Carrie Harper and Marc Jones have asked for the savings proposals - currently out to public consultation - to go before the relevant scrutiny committees so councillors can challenge the plans more fully.
The decision was made after council leader Mark Pritchard invited councillors to scrutinise the proposals by asking for them to be put on the agenda for the various scrutiny committees.
Cllr Marc Jones said:
"Proposed savings that affect the council's economy, business and investment strategy will be looked into by that scrutiny committee next month. Other planned cuts in housing, environment, life-long learning and other departments will also come under scrutiny.
"Councillors have been presented with some information at workshops on the budget but this has often consisted of a sentence saying X thousands would be saved by merging services with other councils or charging service users more. We need to be clear that when we vote on the budget, those figures are credible and what impacts those proposed cuts and increased charges will have.
"That will enable us, as a group, to come up with alternatives to the 'Difficult Decisions' proposals. There are some things - for example charging councillors to park in the Guildhall carpark - that are long overdue but other cuts will have a damaging effect on the borough and will be resisted."