THERE'S been no honeymoon period for the new state government with support sliding for the Liberal Party, according to the latest polling.
The first EMRS poll of state voter intentions released since the March election, shows support for the Liberals has dropped to 48 per cent - its lowest level since May 2011.
That's down from the 51.2 per cent of the primary vote that led to an emphatic election victory.
Poll analyst Kevin Bonham said it would have been hard to improve on the result that delivered the Libs majority government with 15 seats.
"Some new governments get a bit of a boost in the polls but I think they got just about every vote they could get at the election," Dr Bonham said.
"The message that it sends is that it's going to be a challenge for them to hold all their seats.
"They don't have to lose much support to lose a couple of seats."
The poll of 1000 Tasmanians was taken early last week as the tough federal budget dominated the news, which may also have influenced people's voting preferences, Dr Bonham said.
After excluding undecided voters, 25 per cent of EMRS survey respondents' said they would vote Labor - down from the party's 27 per cent primary vote at the election.
State Opposition Leader Bryan Green said he had a lot of work to do.
"What I have to do as Labor leader in Tasmania is make sure I connect with the community, win community trust with respect to the policies that we take forward to the next election," he said.
The Greens were heartened by a massive 7 per cent increase in support since the election, but Dr Bonham said the latest poll result was likely to have overestimated the level of support for the minor party.
Premier Will Hodgman, whose personal approval rating remained strong on 54 per cent, said he would not waste time analysing poll results.
"I'm focused on delivering our agenda," Mr Hodgman said.
However, he had some advice for his political opponents.
"The Greens were fundamentally rejected by Tasmanians (at the election), I don't think they'll be celebrating any minor improvement in polls," he said.
"And for the Labor Party, they are fast becoming a party that is very much about opposition.
"The question for them is how much of the plan that we have a mandate to deliver are they going to continue to oppose?"