Lara Giddings slammed union leaders, accusing them of spreading baseless speculation that Infrastructure Minister David O'Byrne is strategizing a change in leadership following reports that Tasmania's business lobby wants tough budget measures maintained even with a change of premier.

Unionists, on the other hand, say the current direction is heading to a change of premier if Giddings does not back down on budget cuts.

O'Byrne is in a good position in terms of numbers to challenge Giddings, reported ABC News.

Meanwhile, Greens MP Cassy O'Connor has spoken in support of the premier, saying Giddings is doing a good job during tough economic times.

"I do think that under difficult circumstances Lara has tried to do her best by Tasmania and by the Tasmanian people," said O'Connor, who is the latest politician to knock down the leadership change speculation.

Robert Wallace of the Chamber of Commerce and Industry says further investment in the state relies on stable government, and Labor power brokers need to remember that.

"Once they have, if there are any changes in leadership and we're on public notice to be known that we fully support what this government is doing in trying to bring the state back into the black, we certainly would not tolerate anything that was going to put that at risk," he told ABC.

Tasmanian Senator Carol Brown, who spoke out against government plans to close 20 schools as part of budget cuts, has also spoken against a change in leadership, saying it is nothing more than speculation.

"The state government is doing a reasonable job in very hard circumstances," she told ABC.

In reaction, the Community and Public Sector Union's Tom Lynch denies to ABC that there is a conspiracy to remove Giddings from her post.