It wouldn't save much money for the government budget when measured over the long term (perhaps a little due to reduced interest paid on debt/reduced real value of deductions over time & some investors who may not ever make a profit on property to reclaim losses).
The problem I have with it is that it improves the ability for investors to pay more and carry a larger amount of debt than they would have otherwise, pushing up prices and making property less affordable for those buying a home to live in (there does need to be a level of investor activity and not everyone will be able to buy, but there's clearly an excess of speculative investment in some cities at the moment). Negative gearing isn't the only contributing factor though.