There are three major ways in which a budget deficit (total government expenditures exceed total government receipts): borrowing from the public, borrow from the Reserve Bank of Australia (the RBA) or borrow from overseas.
The first involves the selling of government bonds/securities to households and firms, whereby the government offers a rate of interest in return for people's surplus funds. This does not create inflationary tendencies (as the money supply is held constant) and avoids foreign instability that may arise from accumulating foreign debt. However, by adding another investment/savings option into the market, the government provides additional competition in the market, which can force interest rates up. This effect is known as "crowding out". In weaker economic conditions, such as those experienced currently, this crowding out can be amplified, as the private sector is driven out by the government, further slowing already weak private investment and consumption.
The second method is borrowing from the Reserve Bank, so as to increase the money supply in the economy and help finance the shortfall in government revenue. In doing so, this can lead to upward demand-pull inflationary pressures in the economy, if the increase in money supply does not lead to an increase in GDP. If Australia's inflation outlook were weaker than it is currently then this method might be the most appropriate. However given the fact underlying inflation is still 3.9% and unemployment is expected to rise further in coming months, this method may lead to high inflation and slow EG (stagflation) in the local economy if global conditions weaken.
The third method is to borrow from overseas, by way of foreign debt. Foreign debt avoids the internal economic problems discussed above (crowding out and inflation), and can be beneficial in terms of supporting domestic savings to help expand the productive capacity of the economy. However there are costs, by way of rising income remittances (feeding the current account deficits of the future) and the burden and constraints on future governments (and thus taxpayers).
However given Australia's good starting position - negative net public sector debt (i.e. status of "creditor"), responsible borrowing from overseas appears to be the most appropriate method of financing the budget deficit. So long as the debt levels do not rise unsustainably, then the government can avoid the costs of the other two methods (borrowing from the public and the RBA) and sustainably finance the budget deficit of the current downturn, before eventually returning the budget to surplus.