The Herald/Nielsen survey, published by Fairfax on Monday, also shows support for the government has fallen in the past month, due mainly to the asylum seeker issue.
The poll of 1,400 voters found 62 per cent of voters believe the premiers and chief ministers should agree to the health plan.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
In Victoria, support for an agreement was at 58 per cent and 51 per cent in Western Australia.
In NSW, there was 63 per cent support, and in South Australia and Queensland, support was 66 per cent.
Since the previous poll a month ago, primary support for the government has fallen three percentage points to 39 per cent, while the coalition's primary support was steady on 42 per cent.
The survey found Labor's support fell two percentage points to 51 per cent on a two-party preferred basis, while the coalition's rose two points to 49 per cent.
Tony Abbott's personal approval rating fell four points to 46 per cent and his disapproval rating rose four points to 45 per cent.
Mr Rudd leads Mr Abbott as preferred prime minister by 59 per cent to 34 per cent.
His approval rating was 59 per cent and his disapproval rating 36 per cent.
