Whau Local Board member Derek Battersby said councillors should not have the right to abstain from voting.
He said they were paid a salary of $100,000 and ratepayers expected them to take the lead and represent the ratepayers. That was how democracy worked, he said.
Mr Brown looks set to pass his new 10-year, $60 billion budget with less than half the votes of his council at Thursday's governing body meeting.
He will get there after councillors were told the consequences of not passing the budget by chief executive Stephen Town and chief finance officer Sue Tindall over lunch last Thursday.
Councillors attending the lunch said the consequences were dire.
The council would not be able to strike the rates, refinance loans and meet stock exchange requirements.
Mr Town yesterday would not say what he told councillors, only that various "what if" questions had been posed by councillors and "hypothetically what sort of things might occur".
He said debate and votes on the budget were finished.
On Thursday, subject to a final audit opinion, councillors would vote to adopt the new budget and strike the rates.
The mayor is believed to have the support of only seven of the 19 councillors due to attend Thursday's meeting.
His position is weakened by the absence of two supporters - deputy mayor Penny Hulse and John Walker.
Six councillors are expected to vote against the budget - they are Cameron Brewer, Chris Fletcher, Denise Krum, Sharon Stewart, George Wood and Dick Quax.
The other five councillors have serious reservations about the budget.
They particularly object to a targeted rate for transport which takes average household rates increases to 9.9 per cent.
But instead of voting against the budget and plunging the council into crisis, most of the five are expected to abstain to allow the budget to pass.
Labour's Ross Clow said the budget was too regressive and socked it to households and small businesses.
"I'm not going to vote against it but I certainly don't support it," he said.
Mr Walker and Mr Watson are both upset at how the targeted rate of $114 for households was "rammed through" without proper consultation, but hope it will be re-examined next year.
Mr Brewer is planning an amendment calling for the council to instruct Mr Town to commit to a smaller targeted rate of $58.99 contained in this year's budget documents and finding the rest of the funding from within existing budgets when next year's budget comes around.
Mr Brewer said having less than half the council supporting the budget was a political and leadership disaster for Mr Brown.
"That's no political mandate for a 9.9 per cent average residential rates increase.
"Particularly when you consider that more than 80 per cent of submissions on the budget disagreed with even a 3.5 per cent rates increase," he said.
Mr Brown refused to comment yesterday.
How they'll vote
For (8)
Mayor Len Brown
Arthur Anae
Bill Cashmore
Linda Cooper
Chris Darby
Alf Filipaina
Calum Penrose
Penny Webster
Against (6)
Cameron Brewer
Chris Fletcher
Denise Krum
Sharon Stewart
George Wood
Dick Quax
Abstain/uncertain (5)
Cathy Casey
Ross Clow
Mike Lee
Wayne Walker
John Watson
Absent
Penny Hulse
John Walker