The telephone survey of 1000 people statewide earlier this month found that 34 per cent believed Mr Hodgman had the most integrity emerging from the post election machinations and 31 per cent supported Mr McKim.

Only 16 per cent gave Mr Bartlett and his party a tick for integrity, a result showing how the Government took a hit in the polls in the way it managed the minority government negotiations.

For his part Mr McKim seems to have emerged unscathed from his decision to back Labor and accept cabinet posts.

The poll shows that Tasmanians still back either a majority Liberal or Labor government, achieved by another election, over the current minority government arrangement.

It showed that 20 per cent preferred a majority Liberal government, while 17 per cent preferred a Labor majority government.

However, twice as many (13 per cent) preferred a minority Labor government supported by the Greens, with David Bartlett as premier, over the Liberals, with only 6 per cent supporting a Liberal minority government supported by the Greens, with Will Hodgman as premier.

Most of those surveyed, 21 per cent, preferred a second election to determine a clear winner.

The poll showed 37 per cent believing the Liberals best able to provide stable government, to 32 per cent Labor, with only 11 per cent backing the Greens and 16 per cent saying they don't know.

The polling is an important post-election barometer for the Liberals, as Mr Hodgman battles claims that he missed an opportunity to negotiate a minority government deal with the Greens, given that his party won more votes than Labor.

The most recent EMRS opinion poll on party preferences showed Labor's vote crashing further since the election, with the Liberal vote increasing.