The new measures were announced at a press conference at Halifax Town Hall on Wednesday by members of the Liberal Democrat and Conservative groups.
Labour council leader Tim Swit (Town) has issued an urgent call for the leaders of the Conservative and Lib Dem groups to publish the full details of their ‘secret' budget deal.
Coun Swift said: "While the Labour budget proposals have been published for more than four weeks and subject to a great deal of public consultation, the amendments have been put together behind closed doors and revealed tothe press only three daysbefore the annual budget meeting.
"They should publish their full plans so they are open to as much scrutiny as possible in the short time thatremains before the budget has to be decided.
"It's a bit ironic that the Lib Dems have been complaining about there not being enough consultation and they cook this up behind closed doors.
"So far, all we've seen is the video on the Halifax Courier website - local people have the right to know just what is being proposed."
The alternative budget has been denounced as a cynical moveby members of the Labour cabinet.
Cabinet member Daniel Sutherland (Lab, Illingworth and Mixenden) said: "The Lib Dems will jump into bed with anyone - for them it'snot about principles, it's about power.
"They always claim that local government is secretive, but this simply isn't true - it's a line they always fall back on."
It is not just Labour who are frustrated with the proposed amendments, independent councillor Colin Stout (Brighouse) has raised concerns that the coalition can pass the amendments unchallenged.
He said: "It's disgusting and childish the way they've been playing party politics with this.
"The council have been working for months to draw up a budget, and now this coalition has added in their own measures without any consultation - they've shown that they can't be trusted."