The Turnbull government is optimistic it can strike a shock deal with the Senate crossbench and pass the $7.8 billion Medicare levy, one of the centrepiece measures of the 2017 budget.

In a move that defies predictions the 0.5 per cent levy rise would stall in the Senate - and possibly be put on ice until after the next federal election - Treasurer Scott Morrison will on Thursday bring the bill to the Parliament.

The 0.5 per cent levy rise is supposed to start from July 1, 2019 and is designed to help fill the 10-year, $55.7 billion funding shortfall for the National Disability Insurance Scheme.

Mr Morrison has led behind the scenes negotiations with the Greens and members of the Senate crossbench in recent weeks and senior government sources said those meetings had been very "constructive" and the prospect of a deal was a "live option".