In an interview with Fairfax newspapers, the prime minister said she understood some people "would have gotten a bit of a shock" at the way she deposed Kevin Rudd, "and I do understand that they might be looking at me and wondering".
"The only thing I could say to Australians is to judge me on how I do the job," Ms Gillard said. "What we've achieved with the mining industry is one way of showing that I'm very happy to sit down with people and work through difficult issues."
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The resolution to the two-month conflict that had torn down Mr Rudd and brought the government to its knees refuelled speculation of an election being called as early as Sunday.
On to the next task
But Ms Gillard said she had more issues to deal with first, and nominated asylum seeker and population policy as the next priority, followed by climate change.
Before next Thursday she will announce whether to extend a processing freeze on Sri Lankans who arrive by boat and she hinted at changes to migration laws to encourage immigrants to areas where they're needed.
She warned there would be "no quick fix" and rejected suggestions that any toughening of the laws would represent a lurch to the right.
