The Morrison government is preparing to negotiate a $157 million demand from Tasmanian independent Jacqui Lambie to help her state on public housing in return for her vote on sweeping income tax cuts that could be decided on Thursday night.

The government declared it was "happy to engage" in the talks after Senator Lambie called on the federal government to cancel the debt owed by the Tasmanian government for past investments in social housing.

Senator Jacqui Lambie has demanded the Morrison government waive a Tasmanian government debt in return for her vote on income tax cuts. Credit:Dominic Lorrimer

The demand is the first sign of Senator Lambie's willingness to use her new position as a key swing vote in the Senate to extract benefits for her state, maximising her leverage as the fourth and possibly final crossbencher to back the tax plan.

Finance Minister Mathias Cormann responded to her demand on Wednesday afternoon by leaving room to negotiate with Senator Lambie and others.