Yes - she can remain Prime Minister as long as she has ‘the confidence of the House’.
Basically if a majority of members vote her out (76) she has to either resign so her party can choose a new Leader (who will become Prime Minister), or ask the Governor General to dissolve Parliament for another election.
To stay in government with a minority, she needs to get enough independents (and the Green) to agree to support her on ‘confidence and budget motions’ (nothing else) to stop that magic 76 votes against her.
Tony Abbott speaking:
“This is a night for pride in our achievements, for satisfaction at the good results that have been achieved, but above all else mature reflection on the magnitude of the task ahead.”
“Great night for the Australian people.”
“I feel humbled as I feel of the responsibilities that could lie ahead.”
Thanking everybody.
“On current counting, the first ever indigenous member of the House of Representatives will be a Liberal member.”
“I acknowledge my opponent... the last eight weeks could not have been easy for her, and she worked very hard for her cause under difficult circumstances.”
“A win for the Australian people.”
“We do not have a clear result and until we do, the caretaker provisions must continue. What is definitely clear is the Labor Party has definitely lost its majority and what that means is that the government has lost its legitimacy and I say that a government that found it very hard to govern effectively with a makority of 17 seats will never be able to govern with a minority.”
400,000 more people voted for the coalition than for Labor.
Labor achieved lowest primary vote of any government since the second world war.
The Australian people have responded to the clear policies.
Local control of schools and hospitals, practical environment policies, and a strong economy that understands the need of small business.
Australian people have rejected factionalism.
Referendum on the political execution of a Prime Minister - our political system should never be characterised by the midnight knock on the door by the faceless men of the Labor party.
The coalition is back in business.
Stable, predictable, and competent government
Will be talking to the independents.