Nicola Sturgeon is awaiting a response from Lord Freud the UK Minister for Welfare Reform on her call for the cap on discretionary Housing Payments to be lifted.
She wants the Scottish Government to be able to allocate an extra £15m next year which would eliminate the impact of the benefit cut on tenants.
However, the Department of Work and Pensions said extra help it offered had gone unclaimed.
It said £15m of a £20m UK fund is unclaimed and only £1m was allocated to Scots councils after only 11 applied for additional help.
If Lord Freud refuses to lift the cap then the Scottish Government will have to find an alternative method of spending the £15m to mitigate the 'tax'.
An announcement on how that would be achieved would then be likely in John Swinney's budget tomorrow afternoon.
A spokeswoman for the DWP said: "The Scottish Government's call for the current 150% cap on discretionary housing payment top-ups to be increased doesn't fit with our experience of how DHPs are currently working in Scotland.
"The UK Government set aside £20m of additional DHP funding support which local authorities could apply for through a bidding scheme.
"After operating for four months the scheme closes today and so far only 11 Scottish authorities have made a bid for additional funding."
South Lanarkshire, West Dunbartonshire, Renfrewshire, Inverclyde, Fife, North Lanarkshire, Midlothian, Dundee City, West Lothian, North Ayrshire all applied and received a total of £1m from the additional £20m across the UK.